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The Kazhdan-Lusztig Basis and the Temperley-Lieb Quotient in Type D (2000)
| Content Provider | CiteSeerX |
|---|---|
| Author | Losonczy, Jozsef |
| Abstract | : Let H be a Hecke algebra associated with a Coxeter system of type D, and let TL be the corresponding Temperley{Lieb quotient. The algebra TL admits a canonical basis, which facilitates the construction of irreducible representations. In this paper, we explain the relationship between the canonical basis of TL and the Kazhdan{Lusztig basis of H. Key Words: canonical basis; Coxeter group; Hecke algebra; Kazhdan{Lusztig basis; Temperley{Lieb algebra. 2 1. Introduction Let X be a Coxeter graph and let W (X) be an associated Coxeter group with Coxeter generators S(X) and length function `. Let H(X) be the corresponding Hecke algebra. This is an associative, unital algebra over the ring A = Z[v; v 1 ] of Laurent polynomials. The Hecke algebra H(X) has generators T s , one for each s 2 S(X), which are subject to the following relations: T 2 s = (q 1)T s + q, where q = v 2 ; (T s T s 0 ) m = (T s 0 T s ) m if ss 0 has order 2m; and (T s T s 0 ) m T s = (T s 0 T s ) m... |
| File Format | |
| Volume Number | 233 |
| Journal | D, J. Algebra |
| Language | English |
| Publisher Date | 2000-01-01 |
| Access Restriction | Open |
| Subject Keyword | Canonical Basis Hecke Algebra Temperley-lieb Quotient Kazhdan-lusztig Basis Kazhdan Lusztig Basis Corresponding Temperley Lieb Quotient Associated Coxeter Group Coxeter Generator Unital Algebra Coxeter Graph Corresponding Hecke Algebra Introduction Let Temperley Lieb Algebra Irreducible Representation Coxeter Group Coxeter System Algebra Tl Key Word Following Relation Laurent Polynomial |
| Content Type | Text |
| Resource Type | Article |
