Remote Access Representation Theory
Green Open Access

Representation Theory

ISSN 1088-4165

 
 

 

A new basis for the representation ring of a Weyl group


Author: G. Lusztig
Journal: Represent. Theory 23 (2019), 439-461
MSC (2010): Primary 20G99
DOI: https://doi.org/10.1090/ert/534
Published electronically: October 23, 2019
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ W$ be a Weyl group. In this paper we define a new basis for the Grothendieck group of representations of $ W$. This basis contains on the one hand the special representations of $ W$ and on the other hand the representations of $ W$ carried by the left cells of $ W$. We show that the representations in the new basis have a certain bipositivity property.


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

  • [L1] G. Lusztig, A class of irreducible representations of a Weyl group, Nederl. Akad. Wetensch. Indag. Math. 41 (1979), no. 3, 323–335. MR 546372
  • [L2] George Lusztig, Unipotent representations of a finite Chevalley group of type 𝐸₈, Quart. J. Math. Oxford Ser. (2) 30 (1979), no. 119, 315–338. MR 545068, https://doi.org/10.1093/qmath/30.3.315
  • [L3] George Lusztig, Unipotent characters of the symplectic and odd orthogonal groups over a finite field, Invent. Math. 64 (1981), no. 2, 263–296. MR 629472, https://doi.org/10.1007/BF01389170
  • [L4] George Lusztig, A class of irreducible representations of a Weyl group. II, Nederl. Akad. Wetensch. Indag. Math. 44 (1982), no. 2, 219–226. MR 662657
  • [L5] George Lusztig, Characters of reductive groups over a finite field, Annals of Mathematics Studies, vol. 107, Princeton University Press, Princeton, NJ, 1984. MR 742472
  • [L6] George Lusztig, Sur les cellules gauches des groupes de Weyl, C. R. Acad. Sci. Paris Sér. I Math. 302 (1986), no. 1, 5–8 (French, with English summary). MR 827096
  • [L7] G. Lusztig, Leading coefficients of character values of Hecke algebras, The Arcata Conference on Representations of Finite Groups (Arcata, Calif., 1986) Proc. Sympos. Pure Math., vol. 47, Amer. Math. Soc., Providence, RI, 1987, pp. 235–262. MR 933415

Similar Articles

Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2010): 20G99

Retrieve articles in all journals with MSC (2010): 20G99


Additional Information

G. Lusztig
Affiliation: Department of Mathematics, Room 2-365, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email: gyuri@mit.edu

DOI: https://doi.org/10.1090/ert/534
Received by editor(s): January 1, 2400
Received by editor(s) in revised form: January 1, 2019
Published electronically: October 23, 2019
Additional Notes: The author was supported by NSF grant DMS-1566618.
Article copyright: © Copyright 2019 American Mathematical Society