Non-gatherable triples for classical affine root systems

Details Non-gatherable triples for classical affine root systems Non-gatherable triples for classical affine root systems

2010-10-24

arxiv.org/abs/1010.4957v1

Mathematics

Quantum Algebra

Latex, 46 pages

Scientific paper

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.

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