Multiplicities for tensor products on special linear versus classical groups

Special Isogenies and Tensor Product Multiplicities

We show that any bijection between two root systems that preserves angles (but not necessarily lengths) gives rise to inequalities relating tensor product multiplicities for the corresponding complex semisimple Lie groups (or Lie algebras). We explain the inequalities in two ways: combinatorially, using Littelmann's Path Model, and geometrically, using isogenies between algebraic groups defined...

Groups Acting on Tensor Products

Groups preserving a distributive product are encountered often in algebra. Examples include automorphism groups of associative and nonassociative rings, classical groups, and automorphism groups of p-groups. While the great variety of such products precludes any realistic hope of describing the general structure of the groups that preserve them, it is reasonable to expect that insight may be ga...

On the Tensor Products of Modules for Dihedral 2-Groups

The only groups for which all indecomposable modules are ‘knowable’ are those with cyclic, dihedral, semidihedral, and quaternion Sylow p-subgroups. The structure of the Green ring for groups with cyclic and V4 Sylow p-subgroups are known, but no others have been determined. Of the remaining groups, the dihedral 2-groups have the simplest module category but yet the tensor products of any two i...

Tensor Product Multiplicities

THE RATIONAL CHARACTER TABLE OF SPECIAL LINEAR GROUPS

In this paper we will give the character table of the irreducible rational representations of G=SL (2, q) where q= , p prime, n>O, by using the character table and the Schur indices of SL(2,q).