Lucia Morotti
In this paper we completely characterise irreducible tensor products of representations of alternating groups in characteristic 2 of a basic spin module with an irreducible module. This completes the classification of irreducible tensor products of representations of alternating groups.
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In this paper we study irreducible tensor products of representations of alternating groups and classify such products in characteristic 5.
In this paper we completely classify irreducible tensor products of covering groups of symmetric and alternating groups in characteristic $\not=2$.
The Duals of the 2-Modular Irreducible Modules of the Alternating Groups
我们确定特征为2的域上交替群的所有不可约模的对偶模。
In this paper we study irreducible tensor products of representations of alternating groups in characteristics 2 and 3. In characteristic 3 we completely classify irreducible tensor products, while in characteristic 2 we completely classify irreducible tensor products where none of the modules appearing in the product is a basic spin module. In characteristic 2 we also give some necessary conditions for the tensor product of an irreducible module with a basic spin module to be irreducible.
Representations of symmetric and alternating groups and their double covers that remain irreducible modulo every prime
本文分类交错群及其双覆盖的全局不可约表示，并刻画在所有特征下约化几乎齐次或保持不可约的表示，证明除有限例外外它们均为一维或基本旋量表示。
The irreducible representations of the alternating group which remain irreducible in characteristic p
设p是奇素数，An是n次交错群.我们确定了A_n的哪些普通不可约表示在特征p中保持不可约，从而验证了作者在[Represent.理论14，601-626]。鉴于[同前]中所做的筹备工作，我们的任务是确定哪些自共轭划分标记特征p中具有恰好两个合成因子的对称群的Specht模。这是通过使用罗宾逊-布伦丹-Kleshchev“i-限制”函子，连同已知的结果分解数的对称群和额外的结果Mullineux地图和同态之间的Specht模块。
Irreducible spin representations of symmetric and alternating groups which remain irreducible in characteristic 3
本文研究对称群与交错群真双重覆盖的普通不可约自旋表示在特征3下何时仍不可约或齐次，综合归纳限制、次数计算和射影特征分解等方法给出除一类自旋RoCK块相关划分外的分类。
Comparison of Gelfand-Tsetlin Bases for Alternating and Symmetric Groups
杨氏正交基是对称群的不可约表示的经典基。该基恰好是对称群链的Gelfand-Tsetlin基。众所周知，交错群链和对称群链一样，对不可约表示有无重数限制。因此，交错群的每个不可约表示也容许Gelfand-Tsetlin基。此外，每个这样的表示要么是对对称群的不可约表示的限制，要么是对对称群的不可约表示的限制的子表示。在这篇文章中，我们描述了一个递归算法，以写出的对称群的环境表示的杨氏正交基的交替群的不可约表示的每个Gelfand-Tsetlin基向量的扩展。该算法是用Sage数学软件实现的。
For any finite group G it is an interesting question to ask which ordinary irreducible representations of G remain irreducible in a given characteristic p. We answer this question for p=2 when G is the proper double cover of the alternating group. As a key ingredient in the proof, we prove a formula for the decomposition numbers in Rouquier blocks of double covers of symmetric groups, in terms of Schur P-functions.
Representations of the alternating group which are irreducible over subgroups. II
证明了交错群$A_n$的非平凡表示在同构于某个交错群$A_m$的本原真子群上是可约的.
Cyclic Characters of Alternating Groups
本文研究交错群元素在不可约表示中的特征值与循环表示分解，刻画含非零不变向量的配对，并构造新的全局共轭类族以重新证明 Heide–Zalessky 结论。
On the irreducible representation algebra of the alternating group of degree four
给出了2-adic整数环上四次交错群的不可约表示代数的一个刻划。
The irreducible characters of the alternating Hecke algebras
本文计算了交错Hecke代数的不可约特征标，它是交错群的群代数的变形。更确切地说，我们计算的不可约字符的半单交替Hecke代数的一组元素的最小长度共轭类代表的值，我们表明，这些字符值完全确定的不可约字符。作为应用，我们确定了半单交错Hecke代数的分裂域。
We study irreducible restrictions from modules over alternating groups to subgroups. We get reduction results which substantially restrict the classes of subgroups and modules for which this is possible. This is known when the characteristic of the ground field is greater than $3$, but the small characteristics cases require a substantially more delicate analysis and new ideas. In view of our earlier work on symmetric groups we may consider only the restriction of irreducible modules over alternating groups which do not extend to symmetric groups. This work fits into the Aschbacher-Scott progr…
Building on reduction theorems and dimension bounds for symmetric groups obtained in our earlier work, we classify the irreducible restrictions of representations of the symmetric and alternating groups to proper subgroups. Such classification is known when the characteristic of the ground field is greater than $3$, but the small characteristics cases require a substantially more delicate analysis and new ideas. Our results fit into the Aschbacher-Scott program on maximal subgroups of finite classical groups.
On eigenvalues of permutations in irreducible representations of symmetric and alternating groups
本文研究对称群与交错群不可约表示中置换的特征值问题，刻画了复数域上对称群不可约表示下置换的特征值集合，并将结果推广至交错群情形。
Irreducible restrictions of spin representations of symmetric and alternating groups
本文研究代数闭域上几乎拟单群中，限制不可约的子群与模的分类问题，并聚焦于交错群与对称群的 Schur 双覆盖情形。
Irreducible tensor products for symmetric groups in characteristic 2
我们考虑对称群$S_n$的模表示的非平凡不可约张量积，其特征为2，对于偶数$n$，完成了Gow和Kleshchev关于这种乘积的分类猜想的证明。
On the tensor square of irreducible representations of reductive Lie superalgebras
对于特征为零的代数闭域上的半单李超代数，其有限维超表示的范畴是半单的，我们将交错或对称平方表示不可约或分解为不可约表示和平凡表示的不可约超表示分类为一类.
New irreducible tensor product modules for the Virasoro algebra
本文通过对定义在\cite{CG}中的不可约Virasoro模$Ω(λ,α,h)$与定义在\cite{MZ2}中的不可约最高权模$V(θ,h)$或不可约Virasoro模Ind $_θ(N)$作张量积，得到了一类Virasoro模.得到了这类张量积模不可约的充要条件，并确定了其中两个模同构的充要条件。这些模不同构于任何其他已知的不可约Virasoro模。
On tensor products of irreducible integrable representations
本文研究了Cartan矩阵为有限维的Borcherds-Kac-Moody代数的可积范畴$\mathcal{O}$表示，给出了该范畴的不可约表示的张量积同构的充要条件.这个结果推广了C. S. Rajan关于复数上有限维单李代数的有限维不可约表示的张量积的唯一因式分解。
New irreducible tensor product modules for the Virasoro algebra (II)
本文利用不可约Virasoro模$Ω(λ,α,h)$和$Ω(μ, b)$与不可约最高权模$V(θ,h)$或不可约Virasoro模Ind $_θ(N)$的张量积，得到了一类Virasoro模.得到了这类张量积模不可约的充要条件，并确定了其中两个模同构的充要条件。我们还比较了这些模块与其他已知的非重量Virasoro模块。
Decompositions of the tensor products of irreducible sl(2)-modules in characteristic 3
我们完整地描述了特征3中不可约sl（2）-模的张量积的分解（分解成不可分解的子模）.答案类似于李超代数sl（1）的类似分解|1）。
Tensor product of irreducible characters of $\mathrm{GL}_2(\mathbb{F}_q)$
本文分解了奇数 $q$ 下 $\mathrm{GL}_2(\mathbb{F}_q)$ 的两个不可约表示的张量积，分类了无重数和具唯一分解性质的表示对，并刻画了其自对偶不可约表示。
Let $G$ be a simple algebraic group in defining characteristic $p>0$, and let $V$ be an irreducible $G$-module which is the tensor product of exactly two non-trivial modules. We obtain a criterion for $V$ to have the zero weight. In addition, we provide a uniform criterion for an irreducible representation of a simple Lie algebra over the complex numbers to have a multiple of a prescribed fundamental weight.
Semisimple representations of alternating cyclotomic Hecke algebras
我们定义交替分圆Hecke代数在更高的水平作为分圆Hecke代数的子代数下的高盛的哈希对合的模拟。我们计算这些代数的秩，并在半单的情况下构造了一整套不可约表示，推广了Mitsuhashi的结果。
In this paper, we study irreducible weight modules with infinite dimensional weight spaces over the mirror-twisted Heisenberg-Virasoro algebra $\mathcal{D}$. More precisely, the necessary and sufficient conditions for the tensor products of irreducible highest weight modules and irreducible modules of intermediates series over $\mathcal{D}$ to be irreducible are determined by using "shifting technique". This leads to a family of new irreducible weight modules over $\mathcal{D}$. Then we obtain that any two such tensor products are isomorphic if and only if the corresponding highest weight modu…
In this paper, we realize polynomial $\H$-modules $Ω(λ,α,β)$ from irreducible twisted Heisenberg-Virasoro modules $\A_{α,β}$. It follows from $\H$-modules $Ω(λ,α,β)$ and $\mathrm{Ind}(M)$ that we obtain a class of natural non-weight tensor product modules $\big(\bigotimes_{i=1}^mΩ(λ_i,α_i,β_i)\big)\otimes \mathrm{Ind}(M)$. Then we give the necessary and sufficient conditions under which these modules are irreducible and isomorphic, and also give that the irreducible modules in this class are new.
Spin characters of the alternating group which are proportional to linear characters in characteristic 2
分类了交错群的旋量与非旋量不可约特征在2模约化下成比例的情况，等价于在奇阶元上成比例的情况。
Alternating quaternary algebra structures on irreducible representations of sl(2,C)
我们确定了单李代数sl（2，C）的不可约表示V（n）的重数为它的第四外幂$Λ^4 V(n)$的直和项.多重性为1（分别为2)当且仅当n = 4，6（分别n = 8，10）。对于这些n，我们确定了由投影$Λ^4 V(n) \to V(n)$得到的sl（2，C）-不变交替四元代数结构所满足的次数$\le 7$的多线性多项式恒等式。我们将多项式恒等式表示为一个大整数矩阵的零空间，并使用计算线性代数来寻找零空间的标准基。
In this paper, we construct a class of non-weight modules over the affine-Virasoro algebra of type $A_1$ by taking tensor products of irreducibles defined in [Q. Chen, J. Han, Non-weight modules over the affine-Virasoro algebra of type $A_1$, J. Math. Phys. 60, 071707 (2019)] with irreducible highest weight modules. The irreducibility and the isomorphism classes of these modules are determined. Moreover, we show that these tensor product modules are different from the known non-weight modules. Finally, we realize some tensor product modules as induced modules from modules over certain subalgeb…
The aim of this note is to point out a convexity property with respect to the root lattice for the support of the highest weights that occur in a tensor product of irreducible rational representations of $SL(n)$ over the complex numbers. The observation is a consequence of the convexity properties of the saturation cone and the validity of the saturation conjecture for $SL(n)$.
From an irreducible representation of GL(n, C) there is a natural way to construct an irreducible representations of GL(n + 1, C) by adding a zero at the end of the highest weight of the irreducible representation of GL(n, C). The paper considers the decomposition of tensor products of irreducible representation of GL(n, C) and of the corresponding irreducible representations of GL(n + 1, C) and proves a stability result about such tensor products. We go on to discuss similar questions for classical groups.
In this paper, we present a class of non-weight Virasoro modules $\mathcal{M}\big(V,Ω(λ_0,α_0)\big)\otimes\bigotimes_{i=1}^mΩ(λ_i,α_i)$ where $Ω(λ_i,α_i)$ and $\mathcal{M}\big(V,Ω(λ_0,α_0)\big)$ are irreducible Virasoro modules defined in \cite{LZ2} and \cite{LZ} respectively. The necessary and sufficient conditions for $\mathcal{M}\big(V,Ω(λ_0,α_0)\big)\otimes\bigotimes_{i=1}^mΩ(λ_i,α_i)$ to be irreducible are obtained. Then we determine the necessary and sufficient conditions for two such irreducible Virasoro modules to be isomorphic. At last, we show that the irreducible modules in this cla…
A general tensor product theorem
证明了两个局部紧群乘积的每一个容许不可约表示都是其因子的容许不可约表示的张量积。
Existence of a new family of irreducible components in the tensor product and its applications
本文利用晶体理论证明可对称化Kac-Moody代数张量积中存在一类新的不可约分支，并在单李代数且$λ> > μ$条件下完全证明Schur正性猜想。
Irreducible tensor product modules over the Takiff Lie algebra for $\mathfrak{sl}_{2}$
本文研究了Takiff sl₂上不可约张量积模的构造与性质，确定了其不可约性条件及与其他模的区别。
A note on restriction of Characters of Alternating groups to Sylow Subgroups
本文将可被$p$整除的交替群的不可约特征标限制在它们的Sylow $p$ -子群上，并研究了其线性分支的个数。
Decomposition of Tensor Products of Modular Irreducible Representations for $SL_3$: the $p \geq 5$ case
本文研究了两个限制性简单$SL_3(K)$-模的张量积的不可分解直和项的结构，其中$K$是特征$p \geq 5$的代数闭域。我们给出了一个无特征算法的计算这样的张量积分解成不可分解的模块。在作者的早期论文中研究了$\SL_3(K)$的$p<5$情况。在本文中，我们表明，为特点$p\geq 5$所有的不可分解的和是刚性的，在对比的情况下，在特点3。
Labelling the character tables of symmetric and alternating groups
令$X$是对称群$S_n$的特征标表。它表明，除非$n = 4$或$n=6$，有一个独特的方式分配分区的$n$的行和列的$X$，使所有的$λ$和$ν$，$X_{λν}$等于$χ^λ(ν)$，值的不可约特征标的$S_n$标记的$λ$循环类型$ν$的元素。类似的结果证明交替群，并为对称和交替群的布劳尔特征标表。
Huppert's Conjecture for Alternating groups
我们证明了度至少为$5$的交错群是唯一地由它们的不可约复表示的度在一个阿贝尔直因子下确定的。这证实了Huppert关于交替群的猜想。
An irreducible character of a finite group $G$ is called quasi $p$-Steinberg character for a prime $p$ if it takes a nonzero value on every $p$-regular element of $G$. In this article, we classify the quasi $p$-Steinberg characters of Symmetric ($S_n$) and Alternating ($A_n$) groups and their double covers. In particular, an existence of a non-linear quasi $p$-Steinberg character of $S_n$ implies $n \leq 8$ and of $A_n$ implies $n \leq 9$.
Dimensions of irreducible modules for partition algebras and tensor power multiplicities for symmetric and alternating groups
分划代数$\mathsf{P}_k(n)$与对称群$\mathsf{S}_n$在$\mathsf{S}_n$的置换模$\mathsf{M}_n$的$k$ -fold张量幂幂$\mathsf{M}_n^{\otimes k}$上具有Schur-Weyl对偶，因此当$n \ge 2k$时，存在一个满射$\mathsf{P}_k(n) \to \mathsf{Z}_k(n) := \mathsf{End}_{\mathsf{S}_n}(\mathsf{M}_n^{\otimes k}),$，它是一个同构.证明了中心化子代数$\mathsf{Z}_k(n)$的不可约模用第二类Stirling数表示的维数公式。通过Schur-Weyl对偶，这些维数等于$\mathsf{M}_n^{\otimes k}$中不可约$\mathsf{S}_n$ -模的重数。我们的维数表达式适用于任何$n \geq 1$和$k\ge0$。我们的方法是基于模拟的Frobenius互惠，我们显示持有的任意有限群和他们的子群作用于有限维模块的中心化代数。这使我们能够将上述结果推广到划分代数的各种类似物，包括作用于$\mathsf{M}_n^{\otimes k}$的交替群的中心化代数和对应于$\mathsf{S}_n$的反射表示的张量幂的拟划分代数。
Sign conjugacy classes of the alternating groups
有限群$G$的共轭类$C$是一个符号共轭类，如果$G$的每个不可约特征标在$C$上取值0，1或-1.本文对交错群的符号共轭类进行了分类。
Multiplicity-free tensor products of irreducible modules over simple algebraic groups in positive characteristic
该硕士论文针对正特征代数闭域上的单代数群，分类了$SL_2(k)$、$SL_3(k)$及$p=2$时$SL_n(k)$的单模无重数张量积，并给出$Sp_4(k)$的部分结果。
Given a finite group $G$ and a faithful irreducible $FG$-module $V$ where $F$ has prime order, does $G$ have a regular orbit on $V$? This problem is equivalent to determining which primitive permutation groups of affine type have a base of size 2. In this paper, we classify the pairs $(G,V)$ for which $G$ has a regular orbit on $V$ where $G$ is a covering group of a symmetric or alternating group and $V$ is a faithful irreducible $FG$-module such that the order of $F$ is prime and divides the order of $G$.
The q-analogue of the alternating groups and its representations
我们构造了A型Hecke代数的一个子代数。这是交错群的群代数的推广。得到了该子代数的不可约表示的所有等价类以及对称群与交错群的分支规则的q-模拟。
Classification of Irreducible integrable modules for toroidal Lie-algebras with finite dimensional weight spaces
Toroidal李代数是以Laurent多项式为张量的有限维单李代数在多个交换变量上的泛中心扩张。本文对有限维权空间上的Toroidal李代数的不可约可积模进行了分类。它们是有限维李代数的赋值模在中心作用为零时的张量积。在中心作用非平凡的情况下，它们是由Toroidal李代数的自同构扭曲的底层仿射李代数的求值表示的张量积。自同构来自行列式为1或-1的整数的一般线性群。
Unique decomposition of tensor products of irreducible representations of simple algebraic groups
证明了特征为零的域上的简单李代数的有限维不可约表示的张量积唯一地决定了各个成分。这类似于自然数的素数分解的唯一性。
We study the modular representation theory of the symmetric and alternating groups. One of the most natural ways to label the irreducible representations of a given group or algebra in the modular case is to show the unitriangularity of the decomposition matrices, that is, the existence of a unitriangular basic set. We study several ways to obtain such sets in the general case of a symmetric algebra. We apply our results to the symmetric groups and to their Hecke algebras and thus obtain new ways to label the simple modules for these objects. Finally, we show that these sets do not always exis…
Small-dimensional projective representations of symmetric and alternating groups
对最小可能维数和第二最小可能维数的对称和交错群的不可约射影表示进行了分类，并得到了第三最小维数的一个下界.在此过程中，我们得到了一些新的分支结果，可能是独立的利益。
Positivity and the canonical basis of tensor products of finite-dimensional irreducible representations of quantum sl(k)
在量子sl（k）的基本表示的张量积通过最高权范畴的范畴化中，不可分解的倾斜模下降到正则基。由于投射函子将倾斜模映射到倾斜模，有限维不可约表示的张量积在Chevalley生成元作用下的正则基的系数为正.
Tensor product of highest weight modules and intermediate modules for Virasoro algebra have been studied around 1997. Since then the irreducibility problem for tensor product of modules is open. We consider the loop-Virasoro algebra $Vir \otimes B$, where $Vir$ is the Virasoro algebra and $B$ a commutative associative unital algebra over $\mathbb C$. In this paper we study the irreducibility problem for the tensor product of highest weight modules and intermediate modules for $Vir\otimes B$. Finally we find out a necessary and sufficient conditions for such modules to be isomorphic.
In this paper, we construct a class of non-weight modules over the affine-Virasoro algebra of type $A_1$ by taking tensor products of a finite number of irreducible modules $M(λ, α, β, γ)$ with irreducible highest weight modules $V(η, ε, θ)$. We obtain the necessary and sufficient conditions for such tensor product modules to be irreducible, and determine the necessary and sufficient conditions for such two modules to be isomorphic. We also compare these modules with other known non-weight modules, showing that these irreducible modules are new.
Decomposition of tensor products of modular irreducibles for $\SL_2$
利用倾斜模研究了代数群$\SL_2$的两个单模的张量积在正特征下的结构，得到了其不可分解直和项的扭曲张量积定理.其他各种相关的结果，并计算了大量的例子。
Linear groups of alternating type containing non-scalar elements with all but one eigenvalues of multiplicity 1
该研究确定了交错群、对称群及其泛中心扩张中，含除一个特征值外其余特征值重数均为1的非标量元的不可约表示，基域为任意特征的代数闭域。
A new class of irreducible modules over the BMS-Kac-Moody algebra
本文构造BMS-Kac-Moody代数上的新型非权不可约模，给出其不可约及同构的充要条件，经对比证实该类模为新的不可约模。
Tensor product modules over the planar Galilean conformal algebra from free modules of rank one
本文研究平面伽利略共形代数上的不可约张量积模，给出秩为1的Cartan子代数包络代数自由模的张量积不可约的充要条件与同构类，并将结果应用于Witt代数和Heisenberg-Virasoro代数。
Let $G$ be a finite group, and $α$ a nontrivial character of $G$. The McKay graph $\mathcal{M}(G,α)$ has the irreducible characters of $G$ as vertices, with an edge from $χ_1$ to $χ_2$ if $χ_2$ is a constituent of $αχ_1$. We study the diameters of McKay graphs for finite simple groups $G$. For alternating groups, we prove a conjecture made in [LST]: there is an absolute constant $C$ such that $\hbox{diam}\,{\mathcal M}(G,α) \le C\frac{\log |\mathsf{A}_n|}{\log α(1)}$ for all nontrivial irreducible characters $α$ of $\mathsf{A}_n$. Also for classsical groups of symplectic or orthogonal type of …
Specht modules decompose as alternating sums of restrictions of Schur modules
Schur模给出了一般线性群$\mathrm{GL}_t$的不可约多项式表示。将对称群$\mathfrak{S}_t$看作是$\mathrm{GL}_t$的一个子群，我们可以将Schur模限制为$\mathfrak{S}_t$，并将结果分解为Specht模的直和，即$\mathfrak{S}_t$的不可约表示。我们给出了一个等变默比乌斯反演公式，我们用它来反转这种膨胀的代表环$\mathfrak{S}_t$为$t$大。除了明确的公式在体积方面，我们显示的系数出现交替的程度。特别是，这使我们能够定义一个新的基础上的对称函数，其结构常数是稳定的克罗内克系数，并扩大与交替的迹象到舒尔基础。
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