Monomials and temperley-lieb algebras

Abstract

We classify the "fully tight" simply laced Coxeter groups, that is, the ones whose iji-avoiding Kazhdan-Lusztig basis elements are monomials in the generators BSi. We then investigate the basis of the Temperley-Lieb algebra arising from the Kazhdan-Lusztig basis of the associated Hecke algebra, and prove that the basis coincides with the usual (monomial) basis. © 1997 Academic Press.