Remote Access Representation Theory
Green Open Access

Representation Theory

ISSN 1088-4165



On the Kazhdan-Lusztig basis of a spherical Hecke algebra

Author: Friedrich Knop
Journal: Represent. Theory 9 (2005), 417-425
MSC (2000): Primary 20C08
Published electronically: May 13, 2005
MathSciNet review: 2142817
Full-text PDF

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 [Enhancements On Off] (What's this?)

  • [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 $q$-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 of the American Mathematical Society 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

Received by editor(s): March 31, 2004
Received by editor(s) in revised form: March 30, 2005
Published electronically: 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
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society