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Non-Gatherable Triples for Classical Affine Root Systems

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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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Authors and Affiliations

  1. Department of Mathematics, UNC Chapel Hill, North Carolina, 27599, USA

    Ivan Cherednik & Keith Schneider

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  1. Ivan Cherednik
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  2. Keith Schneider
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Correspondence to Ivan Cherednik.

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Partially supported by NSF grants DMS–0800642, DMS–1101535.

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Cherednik, I., Schneider, K. Non-Gatherable Triples for Classical Affine Root Systems. Ann. Comb. 17, 619–654 (2013). https://doi.org/10.1007/s00026-013-0199-0

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  • DOI: https://doi.org/10.1007/s00026-013-0199-0

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