Related papers: On the character tables of the finite reductive gr…

In order to tackle the problem of generically determining the character tables of the finite groups of Lie type $\mathbf{G}(q)$ associated to a connected reductive group $\mathbf{G}$ over $\overline{\mathbb F}_p$, Lusztig developed the…

Let $q$ be a prime power and $F_4(q)$ be the Chevalley group of type $F_4$ over a finite field with $q$ elements. Marcelo--Shinoda (1995) determined the values of the unipotent characters of $F_4(q)$ on all unipotent elements, extending…

Let $G$ be a finite Chevalley group. We are concerned with computing the values of the unipotent characters of $G$ by making use of Lusztig's theory of character sheaves. In this framework, one has to find the transformation between several…

Let ${\mathbb{G}}$ be a simply connected ${\mathbb{Z}}_\ell$-spets, let $q$ be a prime power, prime to $\ell$ and let $S$ be the underlying Sylow $\ell$-subgroup. Firstly, motivated by known formulae for values of Deligne-Lusztig characters…

Let $G$ be a finite group of Lie type. In order to determine the character table of $G$, Lusztig developed the theory of character sheaves. In this framework, one has to find the transformation between two bases for the space of class…

Let $U$ be a Sylow $p$-subgroup of the finite Chevalley group of type $D_4$ over the field of $q$ elements, where $q$ is a power of a prime $p$. We describe a construction of the generic character table of $U$.

We parametrize the set of irreducible characters of the Sylow $p$-subgroups of the Chevalley groups $\mathrm{D}_6(q)$ and $\mathrm{E}_6(q)$, for an arbitrary power $q$ of any prime $p$. In particular, we establish that the parametrization…

Let $G = {\rm U}(2m, {\mathbb F}_{q^2})$ be the finite unitary group, with $q$ the power of an odd prime $p$. We prove that the number of irreducible complex characters of $G$ with degree not divisible by $p$ and with Frobenius-Schur…

We compute the trivial source character tables (also called species tables of the trivial source ring) of the infinite family of finite groups $\text{SL}_{2}(q)$ for $q$ even, over a large enough field $k$ of positive characteristic…

Let $G(q)$ be a Chevalley group over a finite field $F_q$. By Lusztig's and Shoji's work, the problem of computing the values of the unipotent characters of $G(q)$ is solved, in principle, by the theory of character sheaves; one issue in…

Let $\F_q$ be a field of characteristic $p$ with $q$ elements. It is known that the degrees of the irreducible characters of the Sylow $p$-subgroup of $GL_n(\F_q)$ are powers of $q$ by Issacs. On the other hand Sangroniz showed that this is…

We compute the character tables of the following groups with character theoretic methods, using known information about the conjugacy classes and about the character tables of some subgroups and factor groups: $Th$, $J_4$, $2.{}^2E_6(2)$,…

We compute the trivial source character tables (also called species tables of the trivial source ring) of the infinite family of finite groups SL(2,q) over a large enough field of positive characteristic $\ell$ via character-theoretical…

Let $q$ be a power of a prime $p$ and let $U(q)$ be a Sylow $p$-subgroup of a finite Chevalley group $G(q)$ defined over the field with $q$ elements. We first give a parametrization of the set $\text{Irr}(U(q))$ of irreducible characters of…

This survey article is an introduction to some of Lusztig's work on the character theory of a finite group of Lie type $G(F_q)$, where $q$ is a power of a prime~$p$. It is partly based on two series of lectures given at the Centre Bernoulli…

In this article we extend independent results of Lusztig and H\'ezard concerning the existence of irreducible characters of finite reductive groups, (defined in good characteristic and arising from simple algebraic groups), satisfying a…

Let $G$ be a finite reductive group defined over a finite field $F_q$. In the case where $G$ is a special linear group, we compute the multiplicities of irreducible characters of $G(F_{q^2})$ with the character of $G(F_{q^2})$ induced from…

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,…

We construct a supercharacter theory, and establish the supercharacter table for Sylow $p$-subgroups $G_2^{syl}(q)$ of the Chevalley groups $G_2(q)$ of Lie type $G_2$ when $p>2$. Then we calculate the conjugacy classes, determine the…

Let $U(q)$ be a Sylow $p$-subgroup of the Chevalley groups $D_4(q)$ where $q$ is a power of a prime $p$. We describe a construction of all complex irreducible characters of $U(q)$ and obtain a classification of these irreducible characters…