Cellularity of the lowest two-sided ideal of an affine Hecke algebra
arXiv:1302.5204
Abstract
In this paper we show that the lowest two-sided ideal of an affine Hecke algebra is affine cellular for all choices of parameters. We explicitely describe the cellular basis and we show that the basis elements have a nice decomposition when expressed in the Kazhdan-Lusztig basis. In type $A$ we provide a combinatorial description of this decomposition in term of number of paths.
26 pages, 6 figures