|
On the Kazhdan-Lusztig basis of a spherical Hecke algebra
Author(s):
Friedrich
Knop
Journal:
Represent. Theory
9
(2005),
417-425.
MSC (2000):
Primary 20C08
Posted:
May 13, 2005
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
Abstract:
Lusztig proved that the Kazhdan-Lusztig basis of a spherical algebra can be essentially identified with the Weyl characters of the Langlands dual group. We generalize this result to the unequal parameter case. Our new proof is simple and quite different from Lusztig's.
References:
-
- [De]
- Demazure, Michel, Désingularisation des variétés de Schubert généralisées, Ann. Sci. École Norm. Sup. 7 (1974) 53-88. MR 0354697 (50 #7174)
- [Hum]
- Humphreys, J., Reflection groups and Coxeter groups, Cambridge Studies in Advanced Mathematics, 29, Cambridge University Press, Cambridge, 1990. MR 1066460 (92h:20002)
- [KL]
- Kazhdan, D.; Lusztig, G., Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), 165-184. MR 0560412 (81j:20066)
- [Lu1]
- Lusztig, G., Singularities, character formulas, and a
 -analog of weight multiplicities, Analysis and topology on singular spaces, II, III (Luminy, 1981), Astérisque 101-102, Soc. Math. France, Paris, 1983, 208-229. MR 0737932 (85m:17005) - [Lu2]
- Lusztig, G., Affine Hecke algebras and their graded version, J. Amer. Math. Soc. 2 (1989), 599-635. MR 0991016 (90e:16049)
- [Lu3]
- Lusztig, G., Introduction to quantum groups, Progress in Mathematics 110, Birkhäuser, Boston, 1993. MR 1227098 (94m:17016)
- [Mac]
- Macdonald, I., Affine Hecke algebras and orthogonal polynomials, Cambridge Tracts in Mathematics, 157, Cambridge University Press, Cambridge, 2003. MR 1976581 (2005b:33021)
- [NR]
- Nelsen, K.; Ram, A., Kostka-Foulkes polynomials and Macdonald spherical functions, Surveys in Combinatorics, 2003 (C.D. Wensley ed.), London Math. Soc. Lecture Note Ser. 307 Cambridge Univ. Press, Cambridge, 2003, 325-370, math.RT/0401298. MR 2011741 (2004h:05126)
- [Soe]
- Soergel, W., Kazhdan-Lusztig-Polynome und eine Kombinatorik für Kipp-Moduln, Represent. Theory 1 (1997), 37-68. MR 1445511 (99d:17023)
Similar Articles:
Retrieve articles in Representation Theory
with MSC
(2000):
20C08
Retrieve articles in all Journals with MSC
(2000):
20C08
Additional Information:
Friedrich
Knop
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
Email:
knop@math.rutgers.edu
DOI:
10.1090/S1088-4165-05-00237-2
PII:
S 1088-4165(05)00237-2
Received by editor(s):
March 31, 2004
Received by editor(s) in revised form:
March 30, 2005
Posted:
May 13, 2005
Additional Notes:
This work originates from a stay at the University of Strasbourg in 1996 and was finished during a stay at the University of Freiburg in 2003. The author thanks both institutions for their hospitality
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
Comments: webmaster@ams.org