Representation Theory of Polyadic Groups
Wieslaw A. Dudek, Mohammad Shahryari
在这篇文章中，我们引入了多进群的表示的概念，并研究了这些表示与收缩群和覆叠群的表示之间的联系。
In this article, we introduce the notion of representations of polyadic groups and we investigate the connection between these representations and those of retract groups and covering groups.
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Representations of Finite Polyadic Groups
证明了多进群的不可约表示集合与其Post覆盖之间存在一一对应。利用这种对应，我们将有限群中不可约特征标的一些著名性质推广到多进群的情形。
On the Automorphisms and Representations of Polyadic Groups
利用统一的方法，我们确定了任意多进群的自同构和表示的结构。更准确地说，对于一个polyadic组$(G, f)=der_{θ, b}(G, \cdot)$，我们得到了一个完整的描述的自同构和表示的$(G,f)$的自同构和表示的二元组$(G, \cdot)$。
Polyadic systems and their representations are reviewed and a classification of general polyadic systems is presented. A new multiplace generalization of associativity preserving homomorphisms, a 'heteromorphism' which connects polyadic systems having unequal arities, is introduced via an explicit formula, together with related definitions for multiplace representations and multiactions. Concrete examples of matrix representations for some ternary groups are then reviewed. Ternary algebras and Hopf algebras are defined, and their properties are studied. At the end some ternary generalizations …
We suggest a method of constructing special nonunitary representations of semisimple Lie groups using representations of Iwasawa subgroups. As a typical example, we study the group $U(2,2)$.
Imprimitivity theorem for groupoid representations
定义并研究了由各向同性子群胚的表示所诱导的群胚表示的概念。所讨论的广群是局部紧传递拓扑广群。我们制定和证明的imperitivity定理，这样的表示，这是一个推广的经典麦基定理已知的理论群表示。
We list the irreducible two dimensional complex representations of the Braid group B3 in elementary way. Then, we make a decomposition of the square of its irreducible Burau representation.
A character formula for certain representations of loop groups based on non-simply connected Lie groups
基于非单连通李群，计算了环群的某些表示的特征。这给出了Kac-Weyl特征标公式的推广。
Dirac cohomology and unipotent representations of complex groups
本文研究复群的具有Dirac上同调的酉表示，特别是它与幂幺表示的关系
We prove a characterization of monomial projective representations of finitely generated nilpotent groups. We also characterize polycyclic groups whose projective representations are finite dimensional.
In this paper we completely classify irreducible tensor products of covering groups of symmetric and alternating groups in characteristic $\not=2$.
In this paper, we describe a regular representation given by Cayley theorem for 2-crossed modules of groups and their associated Gray 3-group groupoids with a single 0-cell and equivalently cat2-groups.
Some questions about representations of p-adic groups
该研究探讨了与p-adic群表示相关的若干问题，围绕其表示理论展开了讨论。
Necessary and sufficient conditions for a group to possess a faithful irreducible representation are investigated
Exceptional representations of Weyl groups
我们研究了不可约外尔群的例外表示存在的各种后果。（这些是麻省理工学院李群研讨会上的一次演讲的笔记。）
For infinite reductive groups with Frobenius maps, we show that certain subquotients of abstract representations of the groups induced from 1-dimensional representations of Borel subgroups are irreducible.
The purpose of this paper is to give a construction of representations of the group of currents for semisimple groups of rank greater than one. Such groups have no unitary representations in the Fock space, since the semisimple groups of this form have no nontrivial cohomology in faithful irreducible representations. Thus we first construct cohomology of the semisimple groups in nonunitary representations. The principal method is to reduce all constructions to Iwasawa subgroups (solvable subgroups of the semisimple groups), with subsequent extension to the original group. The resulting represe…
Existence of cuspidal representations of p-adic reductive groups
证明了非阿基米德局部域上的任意约化群G都有尖点复表示。
This paper presents the square integrable representations of generalized Weyl-Heisenberg group. We investigate the quasi regular representation of generalized Weyl-Heisenberg group. Moreover, we obtain a concrete from for admissible vector of this representation. Finally, we provide some examples to support our technical considerations.
We show that the irreducible representation of the asymptotic Hecke algebra corresponding to a special representation of a Weyl group admits a basis with strong positivity properties.
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
The special linear representations of compact Lie groups
紧李群G的特殊线性表示是紧李群G的一类具有特殊性质的线性表示。给出了线性表示的积分的定义，并将其推广到特殊的线性表示中，以便于以后的应用。
On the group attached to a special Weyl group representation
本文为 Weyl 群的特殊表示所附加的群提出了一种纯代数的全新定义，替代了 1984 年原基于 Springer 表示理论的几何构造方法。
Algorithms for Representation Theory of Real Reductive Groups
给出了一个计算具有正则积分无穷小特征标的实约化群的不可约容许表示的算法。该算法已在计算机上实现，作为李群和表示项目的一部分。
Irreducible representations of finite spin groups
我们进行必要的计算，以建立一个多重1语句的不可约表示的有限自旋群，这反过来又产生分类的不可约表示的有限自旋群。(The第一个陈述是在没有证据的情况下提出的）。
Errata à ``Sur les représentations non ramifiées des groupes réductifs $p$-adiques; l'exemple de ${\rm GSp}(4)$''
我们纠正两个错误的文件“Sur les représentations non ramifiées des groupes réductifs p-adiques; l 'aple de GSp（4）"：第一个在研究对合的不可约unramified表示的半单群，第二个在描述的陈述组GSp（4）。
We survey different tools to classify representations of compact Lie groups according to their cohomogeneity and apply these methods to the case of irreducible representations of cohomogeneity 6, 7 and 8.
In this note I introduce a new approach to (or rather a new language for) representation theory of groups. Namely, I propose to consider a (complex) representation of a group $G$ as a sheaf on some geometric object (a stack). This point of view necessarily leads to a conclusion that the standard approach to (continuous) representations of algebraic groups is ideologically inconsistent. I propose a way to modify this approach using sheaves on stacks. In new version I corrected some misprints and added an explanation how stack's approach is related to Vogan's picture of representations.
We generalize the Alvis-Curtis duality to the abstract representations of reductive groups with Frobenius maps. Similar to the case of representations of finite reductive groups, we show that the Alvis-Curtis duality of infinite type which we define in this paper also interchanges the irreducible representations in the principal representation category.
We state a conjecture on the reduction modulo the defining characteristic of a unipotent representation of a finite reductive group.
Coxeter groups and the proper joint spectrums of their faithful representations
本文分析了二面体群的忠实表示，证明了Coxeter群可由其忠实表示的真联合谱唯一确定。
Irreducibility of some representations of the groups of symplectomorphisms and contactomorphisms
我们证明了辛同构群和接触同构群的某些酉表示的不可约性。
Let G be a connected reductive group over a field of characteristic zero, and consider an orthogonal representation of G. We give a simple criterion for whether the representation lifts to the spin group, in terms of the highest weights of the irreducible constituents of the representation.
We continue our work on understanding Howe correspondences by using theta representations from p-adic groups to compact groups. We prove some results for unitary theta representations of compact groups with respect to the induction and restriction functors.
In this paper we discuss some of Springer's work on unipotent elements in a reductive groups and on representations of Weyl groups. Among the topics considered are Springer's bijection from the unipotent variety to the nilpotent variety, Springer's example of nonrationality of certain representations of the Hecke algebras associated to a Weyl group and the Springer representation of the Weyl group associated to a unipotent element.
The present paper links the representation theory of Lie groupoids and infinite-dimensional Lie groups. We show that smooth representations of Lie groupoids give rise to smooth representations of associated Lie groups. The groups envisaged here are the bisection group and a group of groupoid self maps. Then representations of the Lie groupoids give rise to representations of the infinite-dimensional Lie groups on spaces of (compactly supported) bundle sections. Endowing the spaces of bundle sections with a fine Whitney type topology, the fine very strong topology, we even obtain continuous and…
This paper investigates the critical group of a faithful representation of a finite group. It computes the order of the critical group in terms of the character values, and gives some restrictions on its subgroup structure. It also computes the precise structure of the critical group both for the regular representation of any finite group, and for the reflection representation of the symmetric group.
Braid group representations from twisted quantum doubles of finite groups
研究了由有限群的扭曲量子偶的表示范畴所产生的辫群表示。对于这些类别，我们表明，由此产生的辫群表示总是通过有限群的因素，在相反的类别与量子群在根的单位。我们还证明了在p-群的情况下，相应的纯辫群表示因子通过有限p-群，这回答了第一作者V. Drinfeld提出的一个问题。
Characters of SL(2) Representations of Groups
我们确定了群和曲面群的SL（2）表示的特征.
An analogue of Burnside's Lemma for 2-transitive groups is shown to hold for a class of topological groups. If the group is compact the representation is finite and splits into an irreducible and the constant functions. If both the group and representation space are noncompact the representation is irreducible
$R$--groups and elliptic representations for similitude groups
研究了特征为零的$p$ \snug -adic群上定义的非退化辛、埃尔米特或分裂正交形式的相似群的回火谱。利用$R$ \snug -群对由真抛物子群的离散级数导出的表示的分支进行了分类.证明了多重性1。确定了调和椭圆谱，并确定了在给定的诱导表示中出现的椭圆特征之间的关系。描述了那些非椭圆的、非完全由椭圆调和表示导出的不可约调和表示。
This paper is dedicated to the study of the stability of multiplicities of group representations.
Linear Representations of the Automorphism Group of a Free Group
设$F_n$是$n\ge 2$元素上的自由群，$\A(F_n)$是它的自同构群.本文给出了$\A(F_n)$的一组丰富的线性表示，它们是由它的有限指数子群在$F_n$的有限商群的关系模上的作用而产生的.我们证明（在某些条件下）我们的表示的图像是算术群。
Fusion Rings of Loop Group Representations
计算了单连通李群的环群的正能量表示的融合环。
On defining characteristic representations of finite reductive groups
给出了李型有限群的不可约表示的定义特征的参数化。
We investigate the question which Q-valued characters and characters of Q-representations of finite groups are Z-linear combinations of permutation characters. This question is known to reduce to that for quasi-elementary groups, and we give a solution in that case. As one of the applications, we exhibit a family of simple groups with rational representations whose smallest multiple that is a permutation representation can be arbitrarily large.
In this article, we study the Schur mutiplier of the discrete as well as the finite Heisenberg groups and their t-variants. We describe the representation groups of these Heisenberg groups and through these give a construction of their finite dimensional complex projective irreducible representations.
Factor Representations of Diffeomorphism Groups
通过与归纳极限酉群的有限因子表示的典范对应，构造了欧氏空间的同态群的一般半有限因子表示.这种构造包括正则对易关系和反对易关系的准自由表示。要建立这种对应关系，需要一种完全积极性的非线性形式，正如阿维森所发展的那样.我们还比较了酉群的渐近特征公式与热力学（$N/V$）极限构造的同构群表示。
The Weil Representations of the Jacobi Group
雅可比群是辛群和海森堡群的半直积。雅可比群是量子力学、几何量子化和光学中的一个重要对象。本文研究Jacobi群的Weil表示及其性质。我们还提供了它们在Jacobi群的自守形式理论和Jacobi群的表示论中的应用。
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.
$R$--groups, elliptic representations, and parameters for $GSpin$ groups
研究了$GSpin_m(F)$的抛物诱导表示，其中$F$是特征为零的$p$ -adic场. Knapp-Stein $R$ -群被描述并证明是初等二群.我们证明了相关的上循环是平凡的，证明了诱导表示的重数为1。我们对椭圆回火谱进行了分类。对于$GSpin_{2n+1}(F)$，我们描述了阿瑟（内窥镜）$R$ -组附加到Langlands参数，并显示这些是同构的相应的Knapp-Stein $R$ -组。
Positive Energy Representations of the Loop Groups of Non Simply Connected Lie Groups
本文分类并构造了紧致、连通、单李群的环群的所有不可约正能量表示，并证明了它们允许Diff（S^{1}）的缠绕作用.
This paper is a sequel to our previous study of spherical representations in the operator algebra setup. We first introduce possible analogs of dimension groups in the present context by utilizing the notion of operator systems and their relatives. We then apply our study to inductive limits of compact quantum groups, and establish an analogue of Olshanski's notion of spherical unitary representations of infinite-dimensional Gelfand pairs of the form $G < G\times G$ (via the diagonal embedding) in the quantum group setup. This, in particular, justifies Ryosuke Sato's approach to asymptotic rep…
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 give a survey of recent developments in the investigation of the various local-global conjectures for representations of finite groups.
In this paper, we introduce two new classes of representations of the framed braid groups. One is the homological representation constructed as the action of a mapping class group on a certain homology group. The other is the monodromy representation of the confluent KZ equation, which is a generalization of the KZ equation to have irregular singularities. We also give a conjectural equivalence between these two classes of representations.
Continuous representations of groupoids
在希尔伯特空间的连续域上引入连续群胚的酉表示.我们调查这些对象的一些属性，并讨论了在这个特定的背景下，从表示论的一些标准结构。正则表示发挥了重要作用。最后，我们讨论了一些算子代数相关的连续表示群胚，特别是，我们分析了连续表示的$G$和连续表示的Banach $*$ -范畴$\hat{L}^{1}(G)$的关系。
We study unitary representations of semidirect products of a compact quantum group with a finite group. We give a classification of all irreducible unitary representations, a description of the conjugate representation of irreducible unitary representations in terms of this classification, and the fusion rules for the semidirect product.
We juxtapose two approaches to the representations of the super-Heisenberg group. Physical one, sometimes called concrete approach, based on the super-wave functions depending on the anti-commuting variables, yielding the harmonic superanalysis and recently developed strict theory of unitary representations of the nilpotent super Lie groups covering the unitary representations of the super-Heisenberg group.
Special representations of nilpotent Lie groups and the associated Poisson representations of current groups
在本文中，我们描述了一个新的模型的表示的电流群与一个半单李群的秩为1。在早期的论文70-80日（荒木，Gelfand-Graev-Vershik）提出了问题的不可约表示的当前组为$SL(2,R)$，并用于这一著名的福克空间结构，建设可以适用于任意局部紧群，是基于所谓的特殊表示的原组$G$，与非平凡1-上同调。利用幂零群的一维扩张（半直积）的特殊性质，给出了一种新的构造方法，该方法可以直接构造出群的特殊表示，然后利用作者以前的文章中的拟Poisson构造方法构造出当前群的表示.秩为1的半单群的抛物子群具有这样的半直积，它的特殊表示可以推广到整个半单群上。从而得到了所需的半单流群的不可约表示的新模型。
Semi-Projective Representations and Twisted Representation Groups
本文将Schur的投射表示群概念推广到代数闭域上的半投射表示，并给出计算机算法，可生成给定有限群在复数域平凡或共轭作用下的所有扭表示群。
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