Related papers: Absolute values and tensor powers of irreducible c…

If chi is an irreducible character of a finite group G then the support of chi is the subset of G on which chi does not vanish. In this note, we study the supports of characters of certain classes of p-groups (a p-group is a finite group of…

In this paper, we present a probabilistic extension of the Fubini polynomials and numbers associated with a random variable satisfying some appropriate moment conditions. We obtain the exponential generating function and an integral…

Let $G$ be a finite $p$-group and $\chi,\psi$ be irreducible characters of $G$. We study the character $\chi\psi$ when $\chi\psi$ has at most $p-1$ distinct irreducible constituents.

Let G be the real points of a simply connected, semisimple, simply laced complex Lie group, and let \tilde{G} be the nonlinear double cover of G. We discuss a set of small genuine irreducible representations of \tilde{G} which can be…

We investigate a beautiful conjecture of T. Wilde on character values and element orders of finite groups. We reduce it to a statement on nearly simple groups that can be checked ``prime by prime". For these groups, we show that a strong…

We study the decomposition of certain reducible characters of classical groups as the sum of irreducible ones. Let ${\mathbf G}$ be an algebraic group of classical type with defining characteristic $p>0$, $\mu$ a dominant weight and $W$ the…

Let G be a finite p-group, for some prime p, and $\psi, \theta \in \Irr(G)$ be irreducible complex characters of G. It has been proved that if, in addition, $\psi,\theta$ are faithful characters, then the product $\psi\theta$ is a multiple…

We consider random character values X(g) of the symmetric group on n symbols, where X is chosen at random from the set of irreducible characters and g is chosen at random from the group, and we show that X(g)=0 with probability tending to…

For an irreducible character $\chi$ of a finite group $G$, let $\mathrm{cod}(\chi):=|G: \ker(\chi)|/\chi(1)$ denote the codegree of $\chi$, and let $\mathrm{cod}(G)$ be the set of irreducible character codegrees of $G$. In this note, we…

In this paper we consider symmetric powers representation and exterior powers representation of finite groups, which generated by the representation which has finite dimension over the complex field. We calculate the multiplicity of…

Let $G$ be a group and $\alpha: G \times G \to G$ denote the commutator map. In the case of finite groups, Frobenius gave the formula to compute the cardinalities of the fibres $\alpha^{-1}(g)$ in terms of the character values $\chi(g)$ for…

Let $G$ be a simple algebraic group in defining characteristic $p>0$, and let $V$ be an irreducible $G$-module which is the tensor product of exactly two non-trivial modules. We obtain a criterion for $V$ to have the zero weight. In…

Let us consider the group $G = < x,y \mid x^m = y^n>$ with $m$ and $n$ nonzero integers. In this paper, we study the variety of epresentations $R(G)$ and the character variety $X(G)$ in $SL(2,\C)$ of the group $G$,obtaining by elementary…

In math.CO/0109093 the author obtained a formula for the value of an irreducible symmetric group character indexed by a partition of rectangular shape. In the present paper this formula is (conjecturally) generalized to arbitrary shapes.

Let $G$ be a finite group of odd order. We show that if $\chi$ is an irreducible primitive character of $G$ then for all primes $p$ dividing the order of $G$ there is a conjugacy class such that the $p-$part of $\chi(1)$ divides the size of…

We construct irreducible unitary representations of a finitely generated free group which are weakly contained in the left regular representation and in which a given linear combination of the generators has an eigenvalue. When the…

We study the solvable groups $G$ that have an irreducible character $\chi\in \Irr(G)$ such that $\chi \bar{\chi}$ has at most two non-principal irreducible constituents.

Let p be a prime number. Let G be a finite p-group and $\chi \in Irr(G)$. Denote by $\bar{\chi} \in Irr(G)$ the complex conjugate of $\chi$. Assume that $\chi(1)=p^n$. We show that the number of distinct irreducible constituents of the…

Recent work has shown that statistical arguments, seemingly well-justified in higher dimensions, can also be used to derive reasonable, albeit less accurate, estimates of the largest Lyapunov exponent ${\chi}$ in lower-dimensional…

In this paper we study finite p-solvable groups having irreducible complex characters chi in Irr(G) which take roots of unity values on the p-singular elements of G.