Non-Gatherable Triples for Non-Affine Root Systems

Details Non-Gatherable Triples for Non-Affine Root Systems Non-Gatherable Triples for Non-Affine Root Systems

2008-09-03

arxiv.org/abs/0809.0534v2

SIGMA 4 (2008), 079, 12 pages

Mathematics

Quantum Algebra

This is a contribution to the Special Issue on Kac-Moody Algebras and Applications, published in SIGMA (Symmetry, Integrabilit

Scientific paper

10.3842/SIGMA.2008.079

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.

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