Let A' be a semisimple algebraic monoid with unit group G. Associated with E is its polyhedral root system (X, 0, C), where X = X(T) is the character group of the maximal torus T c G, $ c X(T) is the set of roots, and C = X(T) is the character monoid of T c E (Zariski closure). The correspondence £-»(A\ O, C) is a complete and discriminating invariant of the semisimple monoid £, extending the w...

For those deformations that satisfy a certain non-degeneracy condition, we describe the structure of simple modules subcharacter algebra finite group. abelian groups, prove deformation given by inclusion natural numbers, which corresponds to generated fibred bisets over field characteristic zero, is not semisimple. In cyclic group prime order case, provide complete description semisimple deform...

In this paper we give a combinatorial characterization of projections of geodesics in Euclidean buildings to Weyl chambers. We apply these results to the representation theory of complex semisimple Lie groups and to spherical Hecke rings associated with nonarchimedean reductive Lie groups. Our main application is a generalization of the saturation theorem of Knutson and Tao for SLn to other com...