Kazhdan–Lusztig Cells and Cellular Bases
The aim of this chapter is to develop a general framework for studying the representation theory of Iwahori-Hecke algebras associated to finite Coxeter groups. Using the Kazhdan-Lustig basis, we give a construction of a cellular basis for the Iwahori-Hecke algebra in the sense of Graham and Lehrer. This gives rise to a general theory of “Specht modules” in which Lusztig’s a-function plays, again, a central role. The chapter ends with an elementary treatment of the case where W is the symmetric group.
KeywordsWeyl Group Parabolic Subgroup Coxeter Group Cell Module Cellular Basis
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