Let S be a connected and simply connected unimodular solvable Lie group, K a connected compact group acting on S as automorphisms. We call the pair (K;S) a Gelfand pair if the Banach -algebra L 1 (KnKnS=K) of allK-biinvariant integrable functions on K n S is commutative. The assumption that (K;S) is a Gelfand pair prescribes the structure of S. For example, if (K;S) is a Gelfand pair, then S is...

For Einstein manifolds with negative scalar curvature admitting an isometric action of a Lie group G \mathsf {G}</mm...

Abstract Zero-divisor codes are constructed using group rings where their generators zero-divisors. Generally, zero-divisor can be equivalent despite associated groups non-isomorphic, leading to the proposed conjecture “Every dihedral code has an form of cyclic code”. This paper is devoted study equivalence in $$F_2G$$ <mml:ms...

The symmetric algebra of a (finite-dimensional) g-module V is the algebra of polynomial functions on the dual space V . Therefore one can study the algebra of symmetric invariants using geometry of G-orbits in V ∗ . In case of the exterior algebra, ∧•V, lack of such geometric picture results by now in absence of general structure theorems for the algebra of skew-invariants (∧•V)g . One may find...

This article expands upon the recent work by Downey, Lempp, and Mileti [3], who classified the complexity of the nilradical and Jacobson radical of commutative rings in terms of the arithmetical hierarchy. Let R be a computable (not necessarily commutative) ring with identity. Then it follows from the definitions that the prime radical of R is Π1, and the Levitzki radical of R is Π 0 2. We show...

Let m be a Levi factor of a proper parabolic subalgebra q of a complex semisimple Lie algebra g. Let t = centm. A nonzero element ν ∈ t is called a t-root if the corresponding adjoint weight space gν is not zero. If ν is a t-root, some time ago we proved that gν is adm irreducible. Based on this result we develop in the present paper a theory of t-roots which replicates much of the structure of...

For a semisimple Lie algebra g the orbit method attempts to assign representations of g to (coadjoint) orbits in g∗. Orbital varieties are particular Lagrangian subvarieties of such orbits leading to highest weight representations of g. In sln orbital varieties are described by Young tableaux. In this paper we consider so called Richardson orbital varieties in sln. A Richardson orbital variety ...