Cellularity of the lowest two-sided ideal of an affine Hecke algebra
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.
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