Keith Schneider | Searcharxiv

arXiv2010

Non-gatherable triples for classical affine root systems

This paper contains a complete description of minimal non-gatherable triangle triples in the lambda-sequences for the affine classical root systems and some claims for arbitrary (reduced) affine root systems. It continues our previous paper devoted to the non-affine case; interestingly, the affine theory clarifies the classification in the non-affine case. The lambda-sequences are associated with reduced decompositions (words) in affine Weyl groups. The existence of the non-gatherable triples is a combinatorial obstacle for using the technique of intertwiners in the theory of irreducible representations of the (double) affine Hecke algebras, complementary to their algebraic-geometric theory.

math.QA↗

arXiv2008

Non-Gatherable Triples for Non-Affine Root Systems

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.

math.QA↗