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Non-Gatherable Triples for Classical Affine Root Systems

Authors
  • Cherednik, Ivan1
  • Schneider, Keith1
  • 1 UNC Chapel Hill, Department of Mathematics, North Carolina, 27599, USA , North Carolina (United States)
Type
Published Article
Journal
Annals of Combinatorics
Publisher
Springer Basel
Publication Date
Aug 20, 2013
Volume
17
Issue
4
Pages
619–654
Identifiers
DOI: 10.1007/s00026-013-0199-0
Source
Springer Nature
Keywords
License
Yellow

Abstract

This paper contains a complete description of minimal non-gatherable triangle triples in the lambda-sequences for the affine classical root systems, as well as certain general claims for arbitrary (reduced) affine root systems. It continues the previous paper of the same authors devoted to the nonaffine case. The lambda-sequences are the sequences of affine positive roots 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 intertwining operators in the theory of irreducible representations of (double) affine Hecke algebras.

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