Hecke Algebras with Unequal Parameters

[CRMMS18] G. Lusztig, Hecke Algebras with Unequal Parameters, 2003
	Contents
	Introduction
	Chapter 1. Coxeter Groups
	Chapter 2. Partial Order on W
	Chapter 3. The Algebra H
	Chapter 4. The Bar Operator
	Chapter 5. The Elements c_w
	Chapter 6. Left or Right Multiplication by c_s
	Chapter 7. Dihedral Groups
	Chapter 8. Cells
	Chapter 9. Cosets of Parabolic Subgroups
	Chapter 10. Inversion
	Chapter 11. The Longest Element for a Finite W
	Chapter 12. Examples of Elements D_w
	Chapter 13. The Function a
	Chapter 14. Conjectures
	Chapter 15. Example: The Split Case
	Chapter 16. Example: The Quasisplit Case
	Chapter 17. Example: The Infinite Dihedral Case
	Chapter 18. The Ring J
	Chapter 19. Algebras with Trace Form
	Chapter 20. The Function a_E
	Chapter 21. Study of a Left Cell
	Chapter 22. Constructible Representations
	Chapter 23. Two-Sided Cells
	Chapter 24. Virtual Cells
	Chapter 25. Relative Coxeter Groups
	Chapter 26. Representations
	Chapter 27. A New Realization of Hecke Algebras
	Bibliography
[Bé] R. Bédard, Cells for two Coxeter groups, Comm. Algebra 14 (1986), 1253-1286.
[Br] K. Bremke, On generalized cells in affine Weyl groups, J. Algebra 191 (1997), 149-173.
[BM] K. Bremke and G. Malle, Reduced words and a length function for G(e,1,n), Indag. Math. (N.S.) 8 (1997), 453-469.
[DL] P. Deligne and G. Lusztig, Representations of reductive groups over finite fields, Ann. of Math. (2) 103 (1976), 103-161.
[Ge] M. Geck, Constructible characters, leading coefficients and left cells for finite Coxeter groups with unequal parameters, Represent. Theory 6 (2002), 1-30.
	1. Introduction
	2. On the generalized left cells of W
	3. Generalized a-invariants and leading coefficients
	4. Orthogonal representations and leading coefficients
	5. Constructible characters and leading coefficients in type Bn
	6. Cells and leading coefficients in type I2(m)
	7. Cells and leading coefficients in type F4
	References
[Ho] P. N. Hoefsmit, Representations of Hecke algebras of finite groups with BN-pairs of classical type, Ph.D. Thesis, Univ. of British Columbia, Vancouver, BC, 1974.
[Iw] N Iwahori, On the structure of the Hecke ring of a Chevalley group over a finite field, J. Fac. Sci. Univ. Tokyo Sect. I 10 (1964), 215-236.
[IM] N. Iwahori and H. Matsumoto, On some Bruhat decomposition and the structure of the Hecke ring of p-adic Chevalley groups, Inst. Hautes Etudes Sci. Publ. Math. 25 (1965), 5-48.
[KL1] D. Kazhdan and G. Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), 165-184.
[KL2] D. Kazhdan and G. Lusztig, Schubert varieties and Poincare duality, Geometry of the Laplace Operator (Honolulu, 1979), Proc. Symp. Pure Math., vol. 36, Amer. Math. Soc., Providence, RI, 1980, pp. 185-203.
[Lu1] G. Lusztig, Coxeter orbits and eigenspaces of Frobenius, Invent. Math. 28 (1976), 101-159.
[Lu2] G. Lusztig, Irreducible representations of finite classical groups, Invent. Math. 43 (1977), 125-175.
[Lu3] G. Lusztig, Left cells in Weyl groups, Lie Group Representations. I, Lecture Notes in Math., vol. 1024, Springer, 1983, pp. 99-111.
[Lu4] G. Lusztig, Some examples of square integrable representations of semisimple p-adic groups, Trans. Amer. Math. Soc. 227 (1983), 623-653.
[Lu6] G. Lusztig, Cells in affine Weyl groups, Algebraic Groups and Related Topics (Kyoto Nagoya, 1983), Adv. Stud. Pure Math., vol. 6, North-Holland, Amsterdam, 1985, pp. 255-287.
[Lu8] G. Lusztig, Cells in affine Weyl groups. II, J. Algebra 109 (1987), 536-548.
[Lu9] G. Lusztig, Introduction to character sheaves, The Arcata Conference on Representations of Finite Groups (Arcata, CA, 1986), Proc. Symp. Pure Math., vol. 47, Amer. Math. Soc., Providence, RI, 1987, pp. 165-180.
[Lu10] G. Lusztig, Intersection cohomology methods in representation theory, Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990), Math. Soc. Japan, Tokyo, 1991, pp. 155-174.
[Lu11] G. Lusztig, Classification of unipotent representations of simple p-adic groups, Internat. Math. Res. Notices (1995), 517-589.
[Lu12] G. Lusztig, Lectures on Hecke algebras with unequal parameters, MIT Lectures, 1999; math.RT 0108172.
[Lu13] G. Lusztig, Classification of unipotent representations of simple p-adic groups. II, Represent. Theory 6 (2002), 243-289; math.RT 0111248.