相关论文: Harish-Chandra series in finite unitary groups and…

We show that the modular branching rule (in the sense of Harish-Chandra) on unipotent modules for finite unitary groups is piecewise described by particular connected components of the crystal graph of well-chosen Fock spaces, under…

This expository paper introduces the theory of Harish-Chandra integrals, a family of special functions that express the integral of an exponential function over the adjoint orbits of a compact Lie group. Originally studied in the context of…

In the modular representation theory of finite unitary groups when the characteristic $\ell$ of the ground field is a unitary prime, the $\hat{\mathfrak{sl}}_e$-crystal on level $2$ Fock spaces graphically describes the Harish-Chandra…

These notes contain an introduction to the theory of complex semisimple quantum groups. Our main aim is to discuss the classification of irreducible Harish-Chandra modules for these quantum groups, following Joseph and Letzter. Along the…

We give conditions for unitarizability of Harish-Chandra super modules for Lie supergroups and superalgebras.

Using Harish-Chandra induction and restriction, we construct a categorical action of a Kac-Moody algebra on the category of unipotent representations of finite unitary groups in non-defining characteristic. We show that the decategorified…

We examine from an algebraic point of view some families of unitary group representations that arise in mathematical physics and are associated to contraction families of Lie groups. The contraction families of groups relate different real…

In this paper, we classify all indecomposable Harish-Chandra modules of the intermediate series over the twisted Heisenberg-Virasoro algebra. Meanwhile, some bosonic modules are also studied.

The non-degenerate spherical principal series of quantum Harish-Chandra modules is constructed. These modules appear in the theory of quantum bounded symmertic domains.

This article is a record of the lecture at the centennial conference for Harish-Chandra. The admissibility theorem of Harish-Chandra concerns the restrictions of irreducible representations to maximal compact subgroups. In this article, we…

Motivated by the maximal subgroup problem of the finite classical groups we begin the classification of imprimitive irreducible modules of finite quasisimple groups. We obtain our strongest results for modules over fields of characteristic…

In this paper, we begin with the classification of Harish-Chandra imprimitive representations in non-defining characteristic. We recall the connection of this problem to certain generalizations of Iwahori-Hecke algebras and show that…

Let $G$ be a semisimple algebraic group over the complex numbers and $K$ be a connected reductive group mapping to $G$ so that the Lie algebra of $K$ gets identified with a symmetric subalgebra of $\mathfrak{g}$. So we can talk about…

Recently the correlation functions of the so-called Itzykson-Zuber/Harish-Chandra integrals were computed (by one of the authors and collaborators) for all classical groups using an integration formula that relates integrals over compact…

We use the progenerator constructed in our previous paper to give a necessary condition for a simple module of a finite reductive group to be cuspidal, or more generally to obtain information on which Harish-Chandra series it can lie in. As…

In this note we discuss the concept of Harish-Chandra modules over the integers. The main result is a rationality result for certain intertwining operator which is used in a joint paper with Raghuram. We also discuss an interesting question…

The main subject of study of this paper are general properties of HarishChandra algebras and modules with respect wito a pair of algebra and subalgebra, with special focus on the transfer properties to a "spherical subalgebra". We also…

We consider the category of Harish-Chandra modules for ${\rm SL}_2(\mathbb R)$ as a module over the category of finite-dimensional representations of ${\rm SL}(2)$ with respect to the tensor product. In this note we use classical results…

We review the categorical representation of a Kac-Moody algebra on unipotent representations of finite unitary groups in non-defining characteristic given by the authors. Then, we extend this construction to finite reductive groups of types…

The irreducible characters of a finite reductive group are partitioned into Harish-Chandra series that are labelled by cuspidal pairs. In this note, we describe how one can algorithmically calculate those cuspidal pairs using results of…