Homogeneous superspaces arising from the general linear supergroup are studied within a Hopf algebraic framework. Spherical functions on homogeneous superspaces are introduced, and the structures of the superalgebras of the spherical functions on classes of homogeneous superspaces are described explicitly.

In recent work, several classes of solitonic solutions of string theory with highermembrane structure have been obtained. These solutions can be classified according to the symmetry possessed by the solitons in the subspace of the spacetime transverse to the membrane. Solitons with four-dimensional spherical symmetry represent instanton solutions in string theory, while those with three-dimensi...

The goal of these lectures is to explain speaker’s results on uniqueness properties of spherical varieties. By a uniqueness property we mean the following. Consider some special class of spherical varieties. Define some combinatorial invariants for spherical varieties from this class. The problem is to determine whether this set of invariants specifies a spherical variety in this class uniquely...

Let G be a simple algebraic group over an algebraically closed field k of bad characteristic. We classify the spherical unipotent conjugacy classes of G. We also show that if the characteristic of k is 2, then the fixed point subgroup of every involutorial automorphism (involution) of G is a spherical subgroup of G.

Let G be a simple algebraic group over an algebraically closed field k of characteristic zero and O be a spherical conjugacy class of G. We determine the decomposition of the coordinate ring k[O] of O into simple G-modules.

We compute the best constants of approximation by entire functions of spherical type and by trigonometric polynomials of spherical degree on classes of functions f satisfying the condition ‖ f ‖Lp 1, where p=1 or 2 and is the Laplace operator. © 2007 Elsevier Inc. All rights reserved.