Related papers: Tensor Power Asymptotics for Linearly Reductive Gr…

Let F be a finite extension of Qp and G be GL(2,F). When V is the tensor product of three admissible, irreducible, finite dimensional representations of G, the space of G-invariant linear forms has dimension at most one. When a non zero…

We consider the periods of the linear congruential and the power generators modulo $n$ and, for fixed choices of initial parameters, give lower bounds that hold for ``most'' $n$ when $n$ ranges over three different sets: the set of primes,…

We give a general asymptotic formula for the growth rate of the number of indecomposable summands in the tensor powers of representations of finite groups, over a field of arbitrary characteristic. In characteristic zero we obtain…

We study infinite groups interpretable in three families of valued fields: $V$-minimal, power bounded $T$-convex, and $p$-adically closed fields. We show that every such group $G$ has unbounded exponent and that if $G$ is dp-minimal then it…

We construct a new family of irreducible unitary representations of a finitely generated virtually free group L. We prove furthermore a general result concerning representations of Gromov hyperbolic groups that are weakly contained in the…

Let $\Gamma$ be a non-commutative free group on finitely many generators. In a previous work two of the authors have constructed the class of multiplicative representations of $\Gamma$ and proved them irreducible as representation of…

For a finite abelian group $G$, the generalized Erd\H{o}s--Ginzburg--Ziv constant $\mathsf s_{k}(G)$ is the smallest $m$ such that a sequence of $m$ elements in $G$ always contains a $k$-element subsequence which sums to zero. If $n =…

We prove that the numbers of irreducible n-dimensional complex continuous representations of the special linear groups over p-adic integers grow slower than the square of n. We deduce that the abscissas of convergence of the representation…

For every finite quasisimple group of Lie type $G$, every irreducible character $\chi$ of $G$, and every element $g$ of $G$, we give an exponential upper bound for the character ratio $|\chi(g)|/\chi(1)$ with exponent linear in $\log_{|G|}…

We consider the semigroup S of highest weights appearing in tensor powers V^k of a finite dimensional representation V of a connected reductive group. We describe the cone generated by S as the cone over the weight polytope of V intersected…

We obtained some sufficient and necessary conditions of existence of faithful irreducible representations of a soluble group $G$ of finite rank over a field $k$. It was shown that the existence of such representations strongly depends on…

An irreducible representation of a reductive Lie algebra, when restricted to a Cartan subalgebra, decomposes into weights with multiplicity. The first part of this paper outlines a procedure to compute symmetric polynomials (e.g., power…

We determine the finite groups whose real irreducible representations have different degrees.

We study when a tensor product of irreducible representations of the symmetric group $S_n$ contains all irreducibles as subrepresentations; we say such a tensor product covers $\mathsf{Irrep}(S_n)$. Our results show that this behavior is…

Let $q$ be a prime power and $U$ the group of lower unitriangular matrices of order $n$ for some natural number $n$. We give a lower bound for the degrees of irreducible constituents of Andr\'{e}-Yan supercharacters and classify the…

Given three irreducible, admissible, infinite dimensional complex representations of GL2(F), with F a local field, the space of trilinear functionals invariant by the group has dimension at most one. When it is one we provide an explicit…

We obtain a complete classification of the continuous unitary representations of oligomorphic permutation groups (those include the infinite permutation group $S_\infty$, the automorphism group of the countable dense linear order, the…

Let $q$ be a power of a prime $p$, $G$ be a finite abelian group, where $p$ does not divide $|G|$,and let $n$ be a positive integer. In this paper we find a formula for the number of irreducible representations of $G$ of a given dimension…

We study the decomposition of tensor powers of two dimensional irreducible representations of quantum $\mathfrak{sl}_2$ at even roots of unity into direct sums of tilting modules. We derive a combinatorial formula for multiplicity of…

The first part of this paper deals with unipotent and reductive groups over finite fields with $q$ elements in which either $q$ goes to infinity or $G=GL_n(q)$ and $n$ goes to infinity. The second part of the paper deals with the symmetric…