Related papers: Trivial source character tables of $\text{SL}_2(q)…

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 $p$ be a prime number. We compute the trivial source character tables of finite Frobenius groups $G$ with an abelian Frobenius complement $H$ and an elementary abelian Frobenius kernel of order $p^2$. More precisely, we deal with all…

We show how the character tables of the groups $E_6(q)_{\text{ad}}$ and ${^2\!E}_6(q)_{\text{ad}}$ can be constructed, where $q$ is a power of~$2$. (Partial results are also obtained for any $q$ not divisible by~$3$.) This is based on…

The rational invariants of the SL_2(q)-invariant quadratic forms on the real irreducible representations are determined. There is still one open question (see Remark 6.5) if q is an even square.

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…

The classification of irreducible, spherical characters of the infinite-dimensional unitary/orthogonal/symplectic groups can be obtained by finding all possible limits of normalized, irreducible characters of the corresponding…

We provide a complete classification of the singularities of cluster algebras of finite type with trivial coefficients. Alongside, we develop a constructive desingularization of these singularities via blowups in regular centers over fields…

Let $G$ be a finite group of even order, let $k$ be an algebraically closed field of characteristic $2$, and let $B$ be a block of the group algebra $kG$ which is of domestic representation type. Up to splendid Morita equivalence, precisely…

In this paper we determine the full character table of a certain split extension $H_1(q)\rtimes Sp(2,q)$ of the Heisenberg group $H_1$ by the odd-characteristic symplectic group $Sp(2,q)$.

We describe the ordinary characters of trivial source modules lying in blocks with cyclic defect groups relying on their recent classification in terms of paths on the Brauer tree by G.~Hiss and the second author. In particular, we show how…

We estimate mixed character sums of polynomial values over elements of a finite field $\mathbb F_{q^r}$ with sparse representations in a fixed ordered basis over the subfield $\mathbb F_q$. First we use a combination of the…

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 obtain nontrivial bounds for character sums with multiplicative and additive characters over finite fields over elements with restricted coordinate expansion. In particular, we obtain a nontrivial estimate for such a sum over a finite…

We classify finite groups with a small average number of zeros in the character table.

We characterize finite-dimensional Lie algebras over an arbitrary field of characteristic zero which admit a non-trivial (quasi-) triangular Lie bialgebra structure.

We prove that the Lie algebra $\mathfrak{sl}_n(\textbf{F}_q)$ of traceless matrices over a finite field of characteristic $p$ can be generated by $2$ elements with exceptions when $(n, p)$ is $(3, 3)$ or $(4,2)$. In the latter cases, we…

We determine character tables for twisted fractional linear groups that form the `other' family in Zassenhaus' classification of finite sharply 3-transitive groups.

We prove that sequentially Cohen-Macaulay rings in positive characteristic, as well as sequentially Cohen-Macaulay Stanley-Reisner rings in any characteristic, have trivial Lyubeznik table. Some other configurations of Lyubeznik tables are…

If the characteristic of a field $k$ is odd any infinitesimal group scheme of $PGL_{2,k}$ lifts to $SL_{2,k}$. In this paper, we prove that this is not true in characteristic $2$ and we give a complete description, up to isomorphism, of…

In this note, we describe a family of particular algebraic, and nonquadratic, power series over an arbitrary finite field of characteristic 2, having a continued fraction expansion with all partial quotients of degree one. The main purpose…