Double Coset Matrices and Group Characters

Representations of Double Coset Lie Hypergroups

We study the double cosets of a Lie group by a compact Lie subgroup. We show that a Weil formula holds for double coset Lie hypergroups and show that certain representations of the Lie group lift to representations of the double coset Lie hypergroup. We characterize smooth (analytic) vectors of these lifted representations.

‎Some‎ relations between ‎$‎L^p‎$‎-spaces on locally compact group ‎$‎G‎$ ‎and‎ double coset $Ksetminus G/H‎$

Let $H$ and $K$ be compact subgroups of locally compact group $G$. By considering the double coset space $Ksetminus G/H$, which equipped with an $N$-strongly quasi invariant measure $mu$, for $1leq pleq +infty$, we make a norm decreasing linear map from $L^p(G)$ onto $L^p(Ksetminus G/H,mu)$ and demonstrate that it may be identified with a quotient space of $L^p(G)$. In addition, we illustrate t...

Group Decomposition by Double Coset Matrices

On the Fischer-Clifford matrices of the non-split extension $2^6{{}^{cdot}}G_2(2)$

The group $2^6{{}^{cdot}} G_2(2)$ is a maximal subgroup of the Rudvalis group $Ru$ of index 188500 and has order 774144 = $2^{12}.3^3.7$. In this paper, we construct the character table of the group $2^6{{}^{cdot}} G_2(2)$ by using the technique of Fischer-Clifford matrices.

Coset Decomposition for Semisimple Hopf Algebras

The notion of double coset for semisimple finite dimensional Hopf algebras is introduced. This is done by considering an equivalence relation on the set of irreducible characters of the dual Hopf algebra. As an application formulae for the restriction of the irreducible characters to normal Hopf subalgebras are given.