Related papers: Harish-Chandra Cuspidal Pairs

Let $G$ be a simple, simply connected algebraic group of exceptional type defined over $\mathbb{F}_q$ with Frobenius endomorphism $F: G \to G$. Let $\ell \nmid q$ be a good prime for $G$. We determine the number of irreducible Brauer…

Recently, Venkatesh extended the category equivalence between affine algebraic groups and Harish-Chandra pairs, which was proved by the author in the supersymmetric context, to the situation of the Verlinde category in positive…

We discuss a practical algorithm to compute parabolic Kazhdan-Lusztig polynomials. As an application we compute Kazhdan-Lusztig polynomials which are needed to evaluate a character formula for reductive groups due to Lusztig. Some…

In this paper we classify the irreducible Harish-Chandra bimodules with full support over filtered quantizations of conical symplectic singularities under the condition that none of the slices to codimension 2 symplectic leaves has type…

As conjectured by T. Przebinda, the transfer of characters in the Howe's correspondence should be obtained via the Cauchy-Harish-Chandra integral. In this paper, we prove that the conjecture holds for the dual pair $(G = U(p, q), G' = U(r,…

Let $\mathfrak{g}$ be a complex semisimple Lie algebra. We give a description of characters of irreducible Whittaker modules for $\mathfrak{g}$ with any infinitesimal character, along with a Kazhdan-Lusztig algorithm for computing them.…

Mathematical physicists have studied degenerations of Lie groups and their representations, which they call contractions. In this paper we study these contractions, and also other families, within the framework of algebraic families of…

Using a general result of Lusztig, we find the decomposition into irreducibles of certain induced characters of the projective general linear group over a finite field of odd characteristic.

We define exact functors from categories of Harish-Chandra modules for certain real classical groups to finite-dimensional modules over an associated graded affine Hecke algebra with parameters. We then study some of the basic properties of…

We prove a generalization of Harish-Chandra's character orthogonality relations for discrete series to arbitrary Harish-Chandra modules for real reductive Lie groups. This result is an analogue of a conjecture by Kazhdan for $\mathfrak…

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…

Let $G$ be a connected reductive group over a finite field $\mathfrak{f}$ of order $q$. When $q$ is small, we make further assumptions on $G$. Then we determine precisely when $G(\mathfrak{f})$ admits irreducible, cuspidal representations…

Let $G_{\mathbb R}$ be the set of real points of a complex linear reductive group and $\hat G_\lambda$ its classes of irreducible admissible representations with infinitesimal integral regular character $\lambda$. In this case each cell of…

In the first chapters, this paper contains a survey on the theory of ordinary characters of finite reductive groups with non-connected centre. The last chapters are devoted to the proof of Lusztig's conjecture on characteristic functions of…

For a semisimple Lie group $G$ satisfying the equal rank condition, the most basic family of unitary irreducible representations is the discrete series found by Harish-Chandra. In this paper, we study some of the branching laws for discrete…

The formal degree of a unipotent discrete series character of a simple linear algebraic group over a non-archimedean local field (in the sense of Lusztig), is a rational function of the cardinality q of the residue field. The irreducible…

By computing reducibility points of parabolically induced representations, we construct, to within at most two unramified quadratic characters, the Langlands parameter of an arbitrary depth zero irreducible cuspidal representation $\pi$ of…

Suppose G is a real reductive Lie group in Harish-Chandra's class. We propose here a structure for the set \Pi_u(G) of equivalence classes of irreducible unitary representations of G. (The subscript u will be used throughout to indicate…

We obtain a classification of simple modules with finite weight multiplicities over basic classical map superalgebras. Any such module is parabolic induced from a simple cuspidal bounded module over a cuspidal map superalgebra. Further on,…

We describe an algorithm for computing Schur indices of irreducible characters of a finite group $G$, based on computations within $G$ and its subgroups and with their character tables. The algorithm has been implemented within \Magma\ and…