Non-Gatherable Triples for Non-Affine Root Systems

Abstract

Abstract. This paper contains a complete description of minimal non-gatherable triangle triples in the lambda-sequences for the classical root systems, F 4 and E 6 . Such sequences are associated with reduced decompositions (words) in affine and non-affine Weyl groups. The existence of the non-gatherable triples is a combinatorial obstacle for using the technique of intertwiners for an explicit description of the irreducible representations of the (double) affine Hecke algebras, complementary to their algebraic-geometric theory.