
SIGMA 4 (2008), 079, 12 pages arXiv:0809.0534
http://dx.doi.org/10.3842/SIGMA.2008.079
Contribution to the Special Issue on KacMoody Algebras and Applications
NonGatherable Triples for NonAffine 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
Abstract
This paper contains a complete description of minimal nongatherable
triangle triples in the lambdasequences for the classical root systems,
F_{4} and E_{6}. Such sequences are associated with reduced decompositions
(words) in affine and nonaffine Weyl groups. The existence of the
nongatherable 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 algebraicgeometric theory.
Key words:
root systems; Weyl groups; reduced decompositions.
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