In this paper we give a simple (local) proof of two principal results about irreducible tempered representations of general linear groups over a non-archimedean local division algebra A. We give a proof of the parameterization of the irreducible square integrable representations of these groups by segments of cuspidal representations, and a proof of the irreducibility of the tempered parabolic ...

We study the Harish-Chandra Schwartz space of an adelic quotient G(F )\G(A). We state a conjectural spectral decomposition of it in terms of parabolic induction. We verify a cuspidal version of this conjecture under additional hypotheses on the group G, which are known to be satisfied for G = GLn.

In this paper we study the some generalization of Jacquet modules of parabolic induction and construct a filtration on it. The successive quotient of the filtration is written by using the twisting functor.

Suppose $p \geq 5$ is a prime number, and let $G = \textrm{SL}_2(\mathbb{Q}_p)$. We calculate the derived functors $\textrm{R}^n\mathcal{R}_B^G(\pi)$, where $B$ Borel subgroup of $G$, $\mathcal{R}_B^G$ right adjoint smooth parabolic induction constructed by Vign\'eras, $\pi$ any smooth, absolutely irreducible, mod $p$ representation $G$.

We prove existence of strong traces at $t=0$ for quasi-solutions to (multidimensional) degenerate parabolic equations with no nondegeneracy conditions. In order solve the problem, we combine blow-up method and a precompactness result induction argument respect space dimension.

We show a connection between Lusztig induction operators in finite general linear and unitary groups and parabolic induction in cyclotomic rational double affine Hecke algebras. Two applications are given: an explanation of a bijection result of Broué, Malle and Michel, and some results on modular decomposition numbers of finite general groups. 2010 AMS Subject Classification: 20C33 Dedicated t...

We study the structure of generalized Verma modules over a semi-simple complex finite-dimensional Lie algebra, which are induced from simple modules over a parabolic subalgebra. We consider the case when the annihilator of the starting simple module is a minimal primitive ideal if we restrict this module to the Levi factor of the parabolic subalgebra. We show that these modules correspond to pr...

A W-algebra is an associative algebra constructed from a semisimple Lie algebra and its nilpotent element. This paper concentrates on the study of 1-dimensional representations of these algebras. Under some conditions on a nilpotent element (satisfied by all rigid elements in exceptional Lie algebras) we obtain a criterium for a finite dimensional module to have dimension 1. It is stated in ter...