|
SIGMA 4 (2008), 079, 12 pages arXiv:0809.0534
https://doi.org/10.3842/SIGMA.2008.079
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
Abstract
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.
pdf (316 kb)
ps (323 kb)
tex (255 kb)
References
- Bourbaki N.,
Groupes et algèbres de Lie, Ch. 4-6,
Hermann, Paris, 1969.
- Cherednik I.,
Non-semisimple Macdonald polynomials. I,
Selecta Math., to appear, arXiv:0709.1742.
- Cherednik I.,
Factorizable particles on a half-line, and root systems,
Teoret. Mat. Fiz. 61 (1984), 35-44 (in Russian).
- Cherednik I.,
Quantum Knizhnik-Zamolodchikov equations and affine
root systems,
Comm. Math. Phys. 150 (1992), 109-136.
- Cherednik I.,
Special bases of irreducible representations of a
degenerate affine Hecke algebra,
Funktsional. Anal. i Prilozhen. 20 (1986), no. 1, 87-88 (in Russian).
- Humphreys J.E.,
Reflection groups and Coxeter groups,
Cambridge Studies in Advanced Mathematics, Vol. 29, Cambridge University Press, Cambridge, 1990.
- Kazhdan D., Lusztig G.,
Proof of the Deligne-Langlands conjecture for Hecke algebras,
Invent. Math. 87 (1987), 153-215.
|
|