| Abstract: Preface: The ultimate goal of this discussion is to provide calculations of some Kazhdan-Lusztig polynomials. Before it is possible to do so, we must cover a considerable amount of material leading up to these wonderful polynomials. We begin by setting up the notions of relflections and roots, upon which all of the material in this volume depend. We then discuss Coxeter groups, followed by Hecke algebras (which have basis elements indexed by Coexeter groups). Through twiddling with Hecke algebras, we find a nice formula for computing Kazhdan-Lusztig polynomials. We follow Humphrey's [8] for the proofs of most of these theorems. Also indispensible was Benson & Grove [2]. The Kazhdan-Lusztig polynomials appearing in the appendices were computed using code developed by Fokko DuCloux. |
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