From groups to symmetric spaces
G. Lusztig
在本文中，我们研究各种属性/结构，这是已知的还原群，我们做了一些实验，看看在何种程度上，他们推广到对称空间。
In this paper we examine various properties/constructions which are known for reductive groups and we do some experiments to see to what extent they generalize to symmetric spaces.
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Greene's Theorem and ideals of the group algebra of a symmetric group
本文利用Greene定理研究对称群群代数，证明相关商环具有群元素自然基，并给出特定置换模零化子的生成元。
In this paper we completely classify irreducible tensor products of covering groups of symmetric and alternating groups in characteristic $\not=2$.
A remark on representations of infinite symmetric groups
我们简化了无限对称群的Thoma表示的构造
Vanishing pairs of conjugacy classes for the symmetric group
本文刻画了对称群中满足任一非线性不可约特征标至少在其一上取零的共轭类对。
Non symmetric quantum loop groups and K-theory
本文通过临界K-理论将Nakajima的对称量子圈群构造推广到任意非对称类型，并给出量子圈群及平移量子圈群部分单模的新几何构造。
We give new, explicit and asymptotically sharp, lower bounds for dimensions of irreducible modular representations of finite symmetric groups.
Generalised row and column removal results for decomposition numbers of spin representations of symmetric groups in characteristic 2
本文在特征2下证明了对称群自旋表示分解数的广义行列删除结果，类比Donkin定理。
On a construction of the basic spin representations of symmetric groups
本文给出了一种构造任意特征域上对称群的双覆盖的基本旋量表示的归纳方法。
A real representation $π$ of a finite group may be regarded as a homomorphism to an orthogonal group $\Or(V)$. For symmetric groups $S_n$, alternating groups $A_n$, and products $S_n \times S_{n'}$ of symmetric groups, we give criteria for whether $π$ lifts to the double cover $\Pin(V)$ of $\Or(V)$, in terms of character values. From these criteria, we compute the second Stiefel-Whitney classes of these representations.
Following the general idea of Schur--Weyl scheme and using two suitable symmetric groups (instead of one), we try to make more explicit the classical problem of decomposing tensor representations of finite and infinite symmetric groups into irreducible components.
Given an odd prime $p$, we identify composition factors of the reduction modulo $p$ of spin irreducible representations of the covering groups of symmetric groups indexed by partitions with 2 parts and find some decomposition numbers.
The Isaacs-Navarro Conjecture for covering groups of the symmetric and alternating groups in odd characteristic
本文证明了由I. M. Isaacs和G. Navarro在2002年提出的关于对称交错群的所有覆叠群，只要$p$是奇素数，都成立.
Sylow subgroups of symmetric and alternating groups and the vertex of $S^{(kp-p,1^p)}$ in characteristic $p$
我们证明了对称群和交错群的Sylow $p$ -子群分别被刻画为$p$ -子群包含所有初等交换$p$ -子群直到对称群和交错群的共轭.在$k \equiv 1$ mod $p$和$k \not\equiv 1$ mod $p^2$的假设下，我们应用对称群的特征结果计算与划分$(kp-p,1^p)$相关联的钩Specht模的顶点.
In this paper, some zeros and non-zeros in the character tables of symmetric groups are displayed in the partition forms. In particular, more zeros of self conjugate partitions beside odd permutations are heavily investigated.
Let $p$ be a prime. In this paper, we compute complexities of some simple modules of symmetric groups labelled by two-part partitions. Most of the simple modules considered here are contained in the $p$-blocks with non-abelian defect groups.
We consider non-trivial irreducible tensor products of modular representations of a symmetric group $S_n$ in characteristic 2 for even $n$ completing the proof of a classification conjecture of Gow and Kleshchev about such products.
A natural representation model for symmetric groups
对于任何正整数$N$，我们在其对合所张成的向量空间上描述对称群$Σ_N$的自然复表示，该对合包含每个不可约表示恰好一次。
Young's orthogonal basis is a classical basis for an irreducible representation of a symmetric group. This basis happens to be a Gelfand-Tsetlin basis for the chain of symmetric groups. It is well-known that the chain of alternating groups, just like the chain of symmetric groups, has multiplicity-free restrictions for irreducible representations. Therefore each irreducible representation of an alternating group also admits Gelfand-Tsetlin bases. Moreover, each such representation is either the restriction of, or a subrepresentation of, the restriction of an irreducible representation of a sym…
The Lie module of the symmetric group
给出了素数特征$p$中$n$字母的对称群的李模的极大投射子模的维数的上界，其中$n = pk$与$p \nmid k$ .
Asymptotyczna teoria reprezentacji grup permutacji (Asymptotic representation theory of symmetric groups)
这篇文章（用波兰语写的）面向广大的数学读者。它的目的是作为一个介绍性的文本有关问题的渐近理论的对称群。
On self-extensions of irreducible modules over symmetric groups, II
本文改进对称群在奇特征域上不可约表示无非平凡自扩张猜想的已有部分结果，提供更多证据。
Vertices of simple modules of symmetric groups labelled by hook partitions
本文研究了素特征$p$中对称群的单模的顶点。特别地，我们完成了简单的$S_n$ -模的顶点标记的钩划分的分类。
Symmetric $k$-varieties are a natural generalization of symmetric spaces to general fields $k$. We study the action of minimal parabolic $k$-subgroups on symmetric $k$-varieties and define a map that embeds these orbits within the orbits corresponding to algebraically closed fields. We develop a condition for the surjectivity of this map in the case of $k$-split groups that depends only on the dimension of a maximal $k$-split torus contained within the fixed point group of the involution defining the symmetric $k$-variety.
A duality of the twisted group algebra of the symmetric group and a Lie superalgebra
设A_k表示对称群S_k的扭群代数，其表示对应于S_k的非线性射影表示.我们建立了A_k与一个李超代数q（n）之间的对偶关系，有时称之为“queer”李超代数.这种对偶性澄清了舒尔公式，就像舒尔-外尔对偶性澄清了弗罗贝纽斯公式一样。
Stability of Restrictions of Representations of the Symmetric Group to the Hyperoctahedral Subgroup
研究对称群表示到超立方体子群限制的稳定性，基于K. Koike和I. Terada的对称函数描述，获得类似经典Murnaghan定理的稳定性结果。
Essén Lectures: Representation Theory of Symmetric Groups
这些是乌普萨拉大学为研究生提供的15个Eugén讲座的部分讲义（在四天内！）在2013年6月。
Character values and decomposition matrices of symmetric groups
利用对称群的普通特征标取值之间的关系，证明了对称群的模表示理论中的两个定理。1.具有奇特征的对称群的分解矩阵具有不同的行。在特征2中，由不同分区$λ$和$μ$标记的分解矩阵的行是相等的，当且仅当$λ$和$μ$是共轭的。对Hecke代数证明了一个类似的结果。2.定义在奇特征的代数闭域上的对称群$S_n$的Specht模在交错群$A_n$的限制下是可分解的当且仅当它是单的，并且标号划分是自共轭的。这个结果被推广到任意域的奇特性。
A conjecture going back to the eighties claims that there are no non-trivial self-extensions of irreducible modules over symmetric groups if the characteristic of the ground field is not equal to $2$. We obtain some partial positive results on this conjecture.
The characters $χ(π)$ of $S_n$ that depend only on the number of cycles of $π$ are completely determined.
A new lower bound on the vertices of Specht modules for the symmetric groups
本文研究了对称群的不可分解Specht模的顶点。对于任意给定的不可分解非投射Specht模，本文的主要定理描述了包含在其顶点中的p-子群族。该定理推广和改进了Wildon在“Vertices of Specht modules and blocks of the对称群“，J. Alg 323（2010）2243- 2256中的早期结果.
Hooks generate the representation ring of the symmetric group
证明了$n$字母上的对称群的表示环由其自然$(n-1)$维表示的外幂生成.我们给出的证明说明了一个由于Y而产生的非常简单的公式。迪维我们提供了一个应用程序，并探讨了可能的推广这一结果的一些其他反射组。
Given a generalized $e$-block $B$ of a symmetric group and an $e$-regular conjugacy class $C$, we study the number of irreducible characters in $B$ which do not vanish on $C$ and find lower bounds for it.
We prove Turner's conjecture, which describes the blocks of the Hecke algebras of the symmetric groups up to derived equivalence as certain explicit Turner double algebras. Turner doubles are Schur-algebra-like `local' objects, which replace wreath products of Brauer tree algebras in the context of the Broué abelian defect group conjecture for blocks of symmetric groups with non-abelian defect groups. The main tools used in the proof are generalized Schur algebras corresponding to wreath products of zigzag algebras and imaginary semicuspidal quotients of affine KLR algebras.
The symmetric group on a set acts transitively on its subsets of a given size. We define homomorphisms between the corresponding permutation modules, defined over a field of characteristic two, which generalize the boundary maps from simplicial homology. The main results determine when these chain complexes are exact and when they are split exact. As a corollary we obtain a new explicit construction of the basic spin modules for the symmetric group.
The 2-modular permutation modules on fixed point free involutions of symmetric groups
本文在偶特征上列举了偶次对称群的置换模中作用于其不动点自由对合集的分量。我们找到每个组件的顶点和Brauer商，以及与每个组件相关联的普通字符。
Morse groups in symmetric spaces corresponding to the symmetric group
本文描述了三个经典对称空间中诣零锥上邻近圈层的Morse群。
A note on the submonoids of the tied-symmetric monoid containing the symmetric group
研究包含对称群的束缚对称幺半群的子幺半群，证明其构成分配格，并确定此类子幺半群的最小生成集。
Character Theory of Symmetric Groups, Subgroup Growth of Fuchsian Groups, and Random Walks
本文给出了任意富克斯群和其它几类大群的子群的渐近展开式。此外，还建立了对称群上随机游动的主要猜想。这两个问题需要微妙的估计特征值和根数的多重性对称群，这也是独立的利益。
Graded Cartan determinants of the symmetric groups
给出了对称群的分次Cartan行列式。在此基础上，我们提出了关于对称群的广义Cartan不变量的Hill猜想的一个阶化，它等价于Külshammer-Olsson-Robinson猜想.
Sign conjugacy classes in symmetric groups
研究了对称群中一类特殊的共轭类，并用它回答了一个关于奇次不可约特征标的问题
On a relation between certain character values of symmetric groups and its connection with creation operators of symmetric functions
本文利用玛雅图，导出了对称群的某些特征标值之间的一种新的关系。我们还研究了我们的结果与Bernstein关于Schur函数的生成算子之间的关系，并通过Schur $Q$ -函数的生成算子考虑了对称群的投射特征标之间的类似关系.我们还考虑了Brauer代数和有壁Brauer代数的特征标之间的相似关系。
A remark on Frobenius characters for set representations of symmetric groups
对于对称群$S_n$的任意集合表示（置换表示），给出了其Frobenius特征标在单项式对称函数基上展开的系数的组合解释.
Elementary divisors of Cartan matrices for symmetric groups
本文给出了对称群的Cartan矩阵的初等因子的一个简单表达式。
The Action of Generalised Symmetric Groups on Symmetric and Exterior Powers of Their Natural Representations
我们建立了广义对称群的自然特征的对称幂所张成的空间的维数的下界。我们采用Savitt和Stanley的方法，从他们的论文“A note on the symmetric powers of the standard representation of $S_n$”（The Electronic Journal of Combinatorics 7（2000），R6）中获得复数和素数特征的界。
Fusion procedure for wreath products of finite groups by the symmetric group
设G是有限群.通过对群环上的有理函数连续求值的融合过程，构造了G与对称群的圈积的两两正交幂等元的完备系统.这个完整的幂等元系统是由标准的杨氏多表索引的。与G与对称群的圈积相联系，定义了对称群的Artin生成元的一种特殊形式，并将其表示在融合过程中所使用的有理函数中.
We explore when generator-conjugate homomorphisms are conjugate and when element-conjugate homomorphisms are conjugate from abelian or dihedral groups to the symmetric group. We completely determine when such homomorphisms are conjugate in the case where the source group has two generators by studying centralizer actions in the target group.
The classification of thick representations of the symmetric group
本文研究对称群在特征为零的域上的厚表示和密集表示的分类，提出新的分类方法和理论框架。
We provide a classification of multiplicity-free inner tensor products of irreducible characters of symmetric groups, thus confirming a conjecture of Bessenrodt. Concurrently, we classify all multiplicity-free inner tensor products of skew characters of the symmetric groups. We also provide formulae for calculating the decomposition of these tensor products.
We study the restriction to the symmetric group, $\mc{S}_n$ of the adjoint representation of $\mt{GL}_n(\C)$. We determine the irreducible constituents of the space of symmetric as well as the space of skew-symmetric $n\times n$ matrices as $\mc{S}_n$-modules.
Multiplicity-free representations of the symmetric group
我们确定了对称群的所有无重数表示。这个项目的动机是一个组合问题，涉及系统的集划分与特定模式的交叉。
A new approach to the representation theory of the symmetric groups. IV. $ \Bbb Z_{2}$-graded groups and algebras
我们从定义一般概念的理论$\Bbb Z_{2}$ -分次代数。然后，我们考虑理论的归纳家庭的$\Bbb Z_{2}$ -分次半单有限维代数及其表示的精神，方法的文件\cite{VO,OV}的表示论的对称群。主要的例子是对称群的射影表示的经典理论.
We relate character theory of the symmetric groups $S_{2n}$ and $S_{2n+1}$ with that of the hyperoctahedral group $B_n = ({\mathbb Z}/2)^n \rtimes S_n$, as part of the expectation that the character theory of reductive groups with diagram automorphism and their Weyl groups, is related to the character theory of the fixed subgroup of the diagram automorphism.
Computing Higher Indicators for the Double of a Symmetric Group
在本文中，我们明确地确定所有指标的Drinfel'd双打的对称群作用于多达10个对象。我们探索不同的字符给出完全相同的指标时，指标有一个零值。我们发现所有的指标都是非负整数，这支持了我们的猜想，即任何对称群的Drinfel'd double的指标都将是非负整数，就像它们对于对称群本身一样。
Exterior and Symmetric Powers of Modules for Cyclic 2-Groups
证明了循环2-群上模的外幂和对称幂的一个递推公式。这使得计算简单明了。以前，一个完整的描述是已知的循环群的素数阶。
Let $G$ be a finite solvable or symmetric group and let $B$ be a $2$-block of $G$. We construct a canonical correspondence between the irreducible characters of height zero in $B$ and those in its Brauer first main correspondent. For symmetric groups our bijection is compatible with restriction of characters.
On the fusion procedure for the symmetric group
本文给出了对称群的融合过程的一个新的版本，它起源于Jucys的工作，由Cherednik发展。我们从对称群的对角矩阵单位的Jucys-Murphy公式导出它。
The Blockwise Navarro Alperin Weight Conjecture for Double Covers of Symmetric and Alternating Groups
本文证明了对称群与交错群双重覆盖的分块 Navarro Alperin 权猜想。
Endotrivial modules for the Schur covers of the symmetric and alternating groups
本文研究了对称群和交错群的Schur覆盖的endovrivial模，并确定了它们的endovrivial模群的结构。我们提供了一个完整的描述，这组发电机和关系在所有情况下。
Markov measures on Young tableaux and induced representations on the infinite symmetric group
证明了在无限Young tableaux空间上，具有单谱的有限对称群的表示的归纳极限类与具有马尔可夫测度的无限对称群的马尔可夫表示类是一致的.证明了由两块Young子群的单位表示导出的无限对称群的表示是Markov表示，并给出了Young图上相应的马尔可夫测度的转移概率的显式表达式.利用有限对称群的诱导双行表示的张量模型，研究了有限对称群的诱导双行表示，得到了相应的Gel'fand-Zetlin基公式.
Sign conjugacy classes of the symmetric 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.本文对对称群的符号共轭类进行了分类，从而验证了Olsson的一个猜想。
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