Representations of surface groups in the projective general linear group

characterization of projective general linear groups

let $g$ be a finite group and $pi_{e}(g)$ be the set of element orders of $g $. let $k in pi_{e}(g)$ and $s_{k}$ be the number of elements of order $k $ in $g$. set nse($g$):=${ s_{k} | k in pi_{e}(g)}$. in this paper, it is proved if $|g|=|$ pgl$_{2}(q)|$, where $q$ is odd prime power and nse$(g)= $nse$($pgl$_{2}(q))$, then $g cong $pgl$_

The Computational Complexity to Evaluate Representations of General Linear Groups

We describe a fast algorithm to evaluate irreducible matrix representations of complex general linear groups GLm with respect to a symmetry adapted basis (Gelfand–Tsetlin basis). This is complemented by a lower bound, which shows that our algorithm is optimal up to a factor m2 with regard to nonscalar complexity. Our algorithm can be used for the fast evaluation of special functions: for instan...

Tensor Representations of the General Linear Super Group

We show a correspondence between tensor representations of the super general linear group GL(m|n) and tensor representations of the general linear superalgebra gl(m|n) constructed by Berele and Regev in [3].

On Characters of Irreducible Unitary Representations of General Linear Groups

Founding harmonic analysis on classical simple complex groups, I.M. Gelfand and M.A. Naimark in their classical book [GN] posed three basic questions: unitary duals, characters of irreducible unitary representations and Plancherel measures. In the case of reductive p-adic groups, the only series of reductive groups where unitary duals are known are general linear groups. In this paper we reduce...

Projective Representations of Generalized Symmetric Groups