On Kazhdan-Lusztig cells in type B
Cédric Bonnafé
DOI: 10.1007/s10801-009-0183-2
Abstract
We prove that, for any choice of parameters, the Kazhdan-Lusztig cells of a Weyl group of type B are unions of combinatorial cells (defined using the domino insertion algorithm).
Pages: 53–82
Keywords: keywords Weyl group; type B; Kazhdan-Lusztig theory; unequal parameters; cells
Full Text: PDF
References
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2. Bonnafé, C.: Semicontinuity properties of Kazhdan-Lusztig cells. Preprint (2008), available at
3. Bonnafé, C., Geck, M., Iancu, L., Lam, T.: On domino insertion and Kazhdan-Lusztig cells in type Bn. Progress in Mathematics (2009, to appear), available at
4. Bonnafé, C., Iancu, L.: Left cells in type Bn with unequal parameters. Represent. Theory 7, 587-609 (2003)
5. Geck, M.: On the induction of Kazhdan-Lusztig cells. Bull. London Math. Soc. 35, 608-614 (2003)
6. Geck, M.: Computing Kazhdan-Lusztig cells for unequal. J. Algebra 281, 342-365 (2004)
7. Geck, M., Pfeiffer, G.: Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras. London Math. Soc. Monographs, New Series, vol.
21. Oxford University Press, London (2000)
8. Kazhdan, D.A., Lusztig, G.: Representations of Coxeter groups and Hecke algebras. Invent. Math. 53, 165-184 (1979)
9. Lam, T.: Growth diagrams, domino insertion, and sign-imbalance. J. Comb. Theory Ser. A. 107, 87- 115 (2004)
10. Lusztig, G.: Left cells in Weyl groups. In: Herb, R.L.R., Rosenberg, J. (eds.) Lie Group Representations I. Lecture Notes in Math., vol. 1024, pp. 99-111. Springer, Berlin (1983)
11. Lusztig, G.: Hecke Algebras with Unequal Parameters. CRM Monograph Series, vol.
18. American Mathematical Society, Providence (2003). 136 p.
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