Related papers: Induced characters of the projective general linea…

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…

We study the irreducible complex representations of general linear groups over principal ideal local rings of length two with a fixed finite residue field. We construct a canonical correspondence between the irreducible representations of…

This paper gives a plethysm formula on the characteristic map of the induced linear characters from the unipotent upper-triangular matrices $U_n(\mathbb F_q)$ to $GL_n(\mathbb F_q)$, the general linear group over finite field $\mathbb F_q$.…

The solvability of monomial groups is a well-known result in character theory. Certain properties of Artin L-series suggest a generalization of these groups, namely to such groups where every irreducible character has some multiple which is…

Let $G$ be a split reductive group over a local field $\bK$, and let $G((t))$ be the corresponding loop group. In \cite{GK} we have introduced the notion of a representation of (the group of $\bK$-points) of $G((t))$ on a pro-vector space.…

K. Harada conjectured for any finite group $G$, the product of sizes of all conjugacy classes is divisible by the product of degrees of all irreducible characters. We study this conjecture when $G$ is the general linear group over a finite…

We study the compositional inverses of some general classes of permutation polynomials over finite fields. We show that we can write these inverses in terms of the inverses of two other polynomials bijecting subspaces of the finite field,…

We give parameterizations of the irreducible representations of finite groups of Lie type in their defining characteristic.

We give a lower bound of the Loewy length of the projective cover of the trivial module for the group algebra $kG$ of a finite group $G$ of Lie type defined over a finite field of odd characteristic $p$, where $k$ is an arbitrary field of…

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…

We continue our study on counting irreducible polynomials over a finite field with prescribed coefficients. We set up a general combinatorial framework using generating functions with coefficients from a group algebra which is generated by…

In his classic book on symmetric functions, Macdonald describes a remarkable result by Green relating the character theory of the finite general linear group to transition matrices between bases of symmetric functions. This connection…

The description of irreducible finite dimensional representations of finite dimensional solvable Lie superalgebras over complex numbers given by V.~Kac is refined. In reality these representations are not just induced from a polarization…

A character of a group is said to be super-monomial if every primitive character inducing it is linear. It is conjectured by Isaacs that every irreducible character of an odd $M$-group is super-monomial. We show that all non linear…

In this paper we consider symmetric powers representation and exterior powers representation of finite groups, which generated by the representation which has finite dimension over the complex field. We calculate the multiplicity of…

We construct an endoscopic decomposition for local L-packets associated to irreducible cuspidal Deligne-Lusztig representations. Moreover, the obtained decomposition is compatible with inner twistings.

We examine which representations of the absolute Galois group of a field of finite characteristic with image over a finite field of the same characteristic may be constructed by the Galois group's action on the division points of an…

We give an algorithm for computing the irreducible admissible representations of a real reductive group with regular integral infinitesimal character. This algorithm has been implemented on a computer, as part of the Atlas of Lie Groups and…

We show the existence of and explicitly construct generic polynomials for various groups, over fields of positive characteristic. The methods we develop apply to a broad class of connected linear algebraic groups defined over finite fields…

We study the intermediate extension of the character sheaves on an adjoint group to the semi-stable locus of its wonderful compactification. We show that the intermediate extension can be described by a direct image construction. As a…