相关论文: A simplified approach to the holomorphic discrete …
Based on the material in an old article of Wallach a short proof of the Harish-Chandra condition is given.
In this paper we generalize Harish Chandra's formula for the formal dimension of a representation of the holomorphic discrete series of a hermitian Lie group $G$ to semisimple symmetric spaces $G/H$.
This paper is a review of results on generalized Harish-Chandra modules in the framework of cohomological induction. The main results, obtained during the last 10 years, concern the structure of the fundamental series of…
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…
We classify the domains of holomorphy of all Harish-Chandra modules of irreducible unitary representations of simple non-compact Lie groups.
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…
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…
A basic exact sequence by Harish-Chandra related to the invariant differential operators on a Riemannian symmetric space G/K is generalized for each K-type in a certain class which we call `single-petaled'. The argument also includes a…
The Slodowy slice is an especially nice slice to a given nilpotent conjugacy class in a semisimple Lie algebra. Premet introduced noncommutative quantizaions of the Poisson algebra of polynomial functions on the Slodowy slice. In this…
Let V be an Harish-Chandra discrete series representation of a real semi-simple Lie group G' and let G be a semi-simple subgroup of G'. In this paper, we give a geometric expression of the G-multiplicities in V when the representation V is…
In this paper, we give a new approach to classify all simple Harish-Chandra modules for the N=1 Ramond algebra based on the so called A-cover theory developed in \cite{BF}
The distribution of the unipotent modules (in non-defining prime characteristic) of the finite unitary groups into Harish-Chandra series is investigated. We formulate a series of conjectures relating this distribution with the crystal graph…
The main result of the paper is a natural construction of the spherical subalgebra in a symplectic reflection algebra associated with a wreath-product in terms of quantum hamiltonian reduction of an algebra of differential operators on a…
We work towards a version of generalized Harish-Chandra theory compatible with Clifford theory and with the action of automorphisms on irreducible characters. This provides a fundamental tool to verify the inductive conditions for the…
Harish-Chandra classified discrete series representations of real semisimple Lie groups by describing their characters as tempered distributions with an explicit formula on the elliptic set. His approach was inspired by Weyl's proof of the…
This is an expository paper which presents the holomorphic classification of rational complex surfaces from a simple and intuitive point of view, which is not found in the literature. Our approach is to compare this classification with the…
In this paper under some conditions we generalize a theorem of Harish-Chandra concerning representability of Fourier transforms of orbital integrals.
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 paper, we classify the simple Harish-Chandra modules over the superconformal current algebra $\widehat{\frak g}$, which is the semi-direct sum of the $N=1$ superconformal algebra with the affine Lie superalgebra $\dot{\frak g}…
We consider symmetric pairs of Lie superalgebras which are strongly reductive and of even type, and introduce a graded Harish-Chandra homomorphism. We prove that its image is a certain explicit filtered subalgebra of the Weyl invariants on…