Related papers: Stein--Sahi complementary series and their degener…

Into this note we collect topics related to homogeneous vector bundles, elliptic adjoint orbits and so forth.

In previous works, we presented series representations for $\pi^3$ and $\pi^5$, in which the prefactor depends only on the golden ratio appears. In this article, we derive a general relation involving trigonometric functions and an infinite…

This paper is a sequel to "Localization of $\frak{u}$-modules. I", hep-th/9411050. We are starting here the geometric study of the tensor category $\cal{C}$ associated with a quantum group (corresponding to a Cartan matrix of finite type)…

There are some new developments on Plancherel formula and growth of matrix coefficients for unitary representations of nilpotent Lie groups. These have several consequences for the geometry of weakly symmetric spaces and analysis on…

We study a class of newly-introduced CFTs associated with even quadratic forms of general signature, which we call generalized Narain theories. We first summarize the properties of these theories. We then consider orbifolds of these…

Given any pair of positive integers m and n, we construct a new Hopf algebra, which may be regarded as a degenerate version of the quantum group of gl(m+n). We study its structure and develop a highest weight representation theory. The…

Hilbert--Lie groups are Lie groups whose Lie algebra is a real Hilbert space whose scalar product is invariant under the adjoint action. These infinite-dimensional Lie groups are the closest relatives to compact Lie groups. Here we study…

This paper develops a basic theory of H-groups. We introduce a special quotient of H-groups and extend some algebraic constructions of topological groups to the category of H-groups and H-maps. We use these constructions to prove some…

Cohesive modules give a dg-enhancement of the bounded derived category of coherent sheaves on a complex manifold via superconnections. In this paper we discuss the deformation theory of cohesive modules on compact complex manifolds. This…

The purpose of this paper is to give an explicit description of the trivial and alternating components of the irreducible representation decomposition of the bigraded module obtained as the tensor square of the coinvariant space for…

We study the modular representation theory of the symmetric and alternating groups. One of the most natural ways to label the irreducible representations of a given group or algebra in the modular case is to show the unitriangularity of the…

We study the structure of minimal parabolic subgroups of the classical infinite dimensional real simple Lie groups, corresponding to the classical simple direct limit Lie algebras. This depends on the recently developed structure of…

Structure monoids and groups are algebraic invariants of equational varieties. We show how to construct presentations of these objects from coherent categorifications of equational varieties, generalising several results of Dehornoy. We…

A real representation $\pi$ 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…

Shimura studied the analytic properties of the non-holomorphic Siegel Eisenstein series and derived a residue formula. Herein, we provide a refinement of his result for several types of Eisenstein series.

The main result of this article is an application of the theory of invariant convex cones of Lie algebras to the study of unitary representations of Lie supergroups. It also includes an exposition of recent results of the second author on…

These notes were prepared for the MSRI hot topics workshop on superstrong approximation (2012). We give a brief overview of the developments in the theory, especially the fundamental expansion theorem. Applications to diophantine problems…

This work hopes to be an introduction to Deligne categories for someone familiar with classical representation theory and some category theory. In the first chapter, we motivate and define (symmetric) tensor categories, construct the…

After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…

A two-parametric deformation of U[sl(2)] and its representations are considered. This newly introduced two-parametric quantum group denoted as $U_{pq}[sl(2)]$ admits a class of infinite-dimensional representations which have no classical…