‎For a homogeneous spaces ‎$‎G/H‎$‎, we show that the convolution on $L^1(G/H)$ is the same as convolution on $L^1(K)$, where $G$ is semidirect product of a closed subgroup $H$ and a normal subgroup $K $ of ‎$‎G‎$‎. ‎Also we prove that there exists a one to one correspondence between nondegenerat $ast$-representations of $L^1(G/H)$ and representations of ...

We generalize the notion of a projective profinite group to a projective pair of a profinite group and a closed subgroup. We establish the connection with Pseudo Algebraically Closed (PAC) extensions of PAC fields: Let M be an algebraic extension of a PAC field K. Then M/K is PAC if and only if the corresponding pair of absolute Galois groups (Gal(M),Gal(K)) is projective. Moreover any projecti...

Introduction Let G be a connected reductive group over an algebraically closed eld k; let B G be a Borel subgroup and K G a closed subgroup. Assume that K is a spherical subgroup of G, that is, the number of K-orbits in the ag variety G=B is nite; equivalently, the set KnG=B of (K; B)-double cosets in G is nite. Then the following problems arise naturally.

In this paper, we introduce the concept of strongly binary g^⋆-closed sets in topological space and investigate group structure set all