Related papers: Green functions and higher Deligne--Lusztig charac…
Based on results of Digne-Michel-Lehrer (2003) we give two formulae for two-variable Green functions attached to Lusztig induction in a finite reductive group. We present applications to explicit computation of these Green functions, to…
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…
Under a largeness assumption on the size of the residue field, we give an explicit description of the positive-depth Deligne--Lusztig induction of unramified elliptic pairs $(T,\theta)$. When $\theta$ is regular, we show that positive-depth…
Lusztig's algorithm of computing generalized Green functions of reductive groups involves an ambiguity of certain scalars. In this paper, for reductive groups of classical type with arbitrary characteristic, we determine those scalars…
In this paper we study higher level Deligne--Lusztig representations of reductive groups over discrete valuation rings, with finite residue field $\mathbb{F}_q$. In previous work we proved that, at even levels, these geometrically…
Lusztig has given a construction of certain representations of reductive groups over finite local principal ideal rings of characteristic p, extending the construction of Deligne and Lusztig of representations of reductive groups over…
Let $G(q)$ be a finite group of Lie type over a field with $q$ elements, where $q$ is a prime power. The Green functions of $G(q)$, as defined by Deligne and Lusztig, are known in \textit{almost} all cases by work of Beynon--Spaltenstein,…
In this paper we propose a construction of generic character sheaves on reductive groups over finite local rings at even levels, whose characteristic functions are higher Deligne--Lusztig characters when the parameters are generic. We…
We extend the classical result asserting that the twisting operator preserves certain Deligne--Lusztig character values for truncated formal power series; along the way we discuss some properties of centralisers. This leads us to the…
We determine the Lusztig restrictions on the space of class functions with a unipotent support on a finite reductive group. In particular we give a simple expression for the Lusztig restrictions of the generalized Green functions and we…
The 2-parameter Green functions occur as a crucial ingredient in the character formula for Lusztig induction in finite reductive groups. Still, very little is known about these functions, in particular in the case of groups arsing from…
We prove a character formula for some closed fine Deligne-Lusztig varieties. We apply it to compute fixed points for fine Deligne-Lusztig varieties arising from the basic loci of Shimura varieties of Coxeter type. As an application, we…
In a previous paper, "Generalized Green functions and unipotent classes for finite reductive groups, I", we have determined certain unknown scalars involved in the algorithm of computing generalized Green functions in the case of SL_n. In…
The Glauberman correspondence is a fundamental bijection in the character theory of finite groups. In 1994, Hartley and Turull established a degree-divisibility property for characters related by that correspondence, subject to a congruence…
In this paper, we consider the set of r-symbols in a full generality. We construct Hall-Littlewood functions and Kostka functions associated to those r-symbols. We also discuss a multi-parameter version of those functions. We show that…
This article is devoted to deduce the expression of the Green's function related to a general constant coefficients fractional difference equation coupled to Dirichlet conditions. In this case, due to the points where some of the fractional…
Given a connected reductive group $\tilde{G}$ over a finite field $k$, and a semisimple $k$-automorphism $\varepsilon$ of $\tilde{G}$ of finite order, let $G$ denote the connected part of the group of $\varepsilon$-fixed points. Then there…
Based on a canonical approach and functional-integration techniques, a series expansion of Green's function of a scalar field, in the presence of a medium, is obtained. A series expansion for Lifshitz-energy, in finite-temperature, in terms…
In a previous paper it was shown that a certain family of varieties suggested by Lusztig, is not enough to construct all irreducible complex representations of reductive groups over finite rings coming from the ring of integers in a local…
Edelman and Greene generalized the Robinson--Schensted--Knuth correspondence to reduced words in order to give a bijective proof of the Schur positivity of Stanley symmetric functions. Stanley symmetric functions may be regarded as the…