Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 4 (2008), 079, 12 pages      arXiv:0809.0534
Contribution to the Special Issue on Kac-Moody Algebras and Applications

Non-Gatherable Triples for Non-Affine Root Systems

Ivan Cherednik and Keith Schneider
Department of Mathematics, UNC Chapel Hill, North Carolina 27599, USA

Received September 03, 2008, in final form November 08, 2008; Published online November 14, 2008

This paper contains a complete description of minimal non-gatherable triangle triples in the lambda-sequences for the classical root systems, F4 and E6. 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.

Key words: root systems; Weyl groups; reduced decompositions.

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