Related papers: Generalised Gelfand-Graev Representations in Small…

Let $G$ be a connected reductive algebraic group defined over a finite field with $q$ elements. In the 1980's, Kawanaka introduced generalised Gelfand-Graev representations of the finite group $G(F_q)$, assuming that $q$ is a power of a…

For a connected reductive algebraic group $G$ defined over a finite field $\mathbb F_q$, Kawanaka introduced the generalized Gelfand-Graev representations (GGGRs for short) of the finite group $G(\mathbb F_q)$ in the case where $q$ is a…

Let $G$ be a connected reductive algebraic group defined over the finite field $\F_q$, where $q$ is a power of a good prime for $G$, and let $F$ denote the corresponding Frobenius endomorphism, so that $G^F$ is a finite reductive group. Let…

Assume $G$ is a connected reductive algebraic group defined over $\bar{\mathbb{F}_p}$ such that $p$ is good prime for $G$. Furthermore we assume that $Z(G)$ is connected and $G/Z(G)$ is simple of classical type. Let $F$ be a Frobenius…

Let $G$ be a connected reductive algebraic group defined over a finite field $\mathbb{F}_q$. In the 1980s, Kawanaka introduced the generalized Gelfand-Graev representations (GGGRs for short) of the finite group $G^F$ in the case where $q$…

Let $G$ be a connected reductive group defined over a finite field $\mathbb{F}_q$ of characteristic $p$, with Deligne--Lusztig dual $G^\ast$. We show that, over $\overline{\mathbb{Z}}[1/pM]$ where $M$ is the product of all bad primes for…

Let $G$ be a simple algebraic group defined over a finite field of good characteristic, with associated Frobenius endomorphism $F$. In this article we extend an observation of Lusztig, (which gives a numerical relationship between an…

Let $G$ be a connected reductive group over $F_q$, where $q$ is large enough and the center of $G$ is connected. We are concerned with Lusztig's theory of {\em character sheaves}, a geometric version of the classical character theory of the…

Assume $\mathbf{G}$ is a connected reductive algebraic group defined over an algebraic closure $\mathbb{K} = \overline{\mathbb{F}}_p$ of the finite field of prime order $p>0$. Furthermore, assume that $F : \mathbf{G} \to \mathbf{G}$ is a…

Recently, a strong exponential character bound has been established in [3] for all elements $g \in \mathbf{G}^F$ of a finite reductive group $\mathbf{G}^F$ which satisfy the condition that the centraliser $C_{\mathbf{G}}(g)$ is contained in…

Let G be a connected reductive group defined over an algebraically closed field k of characteristic p > 0. The purpose of this paper is two-fold. First, when p is a good prime, we give a new proof of the ``order formula'' of D. Testerman…

With a view to determining character values of finite reductive groups at unipotent elements, we prove a number of results concerning inner products of generalised Gelfand-Graev characters with characteristic functions of character sheaves,…

Let G be any connected reductive group over a non-archimedean local field. We analyse the unipotent representations of G, in particular in the cases where G is ramified. We establish a local Langlands correspondence for this class of…

Let $G$ be a finite reductive group defined over $\mathbb{F}_q$, with $q$ a power of a prime $p$. Motivated by a problem recently posed by C. Curtis, we first develop an algorithm to express each element of $G$ into a canonical form in…

Let G be a connected reductive group over a non-archimedean local field K, and assume that G splits over an unramified extension of K. We establish a local Langlands correspondence for irreducible unipotent representations of G. It comes as…

Let G be a reductive linear algebraic group over an algebraically closed field of characteristic p > 0. A subgroup of G is said to be separable in G if its global and infinitesimal centralizers have the same dimension. We study the…

Let $F$ be a non-Archimedean locally compact field, let $G$ be a split connected reductive group over $F$. For a parabolic subgroup $Q\subset G$ and a ring $L$ we consider the $G$-representation on the $L$-module$$(*)\quad\quad\quad\quad…

The work of Bernstein-Zelevinsky and Zelevinsky gives a good understanding of irreducible subquotients of a reducible principal series representation of $GL_n(F)$, $F$ a $p$-adic field (without specifying their multiplicities which is done…

The Gan-Gross-Prasad problem is to describe the restriction of representations of a classical group $G$ to smaller groups $H$ of the same kind. In this paper, we solved the Gan-Gross-Prasad problem over finite fields completely. In previous…

Let $G$ be a simple simply-connected algebraic group over an algebraically closed field $k$ of characteristic $p>0$ with $\mathfrak{g}={\rm Lie}(G)$. We discuss various properties of nilpotent orbits in $\mathfrak{g}$, which have previously…