Mask formulas for cograssmannian Kazhdan-Lusztig polynomials

Details Mask formulas for cograssmannian Kazhdan-Lusztig polynomials Mask formulas for cograssmannian Kazhdan-Lusztig polynomials

2010-11-04

arxiv.org/abs/1011.1110v1

Mathematics

Combinatorics

43 pages

Scientific paper

We give two contructions of sets of masks on cograssmannian permutations that can be used in Deodhar's formula for Kazhdan-Lusztig basis elements of the Iwahori-Hecke algebra. The constructions are respectively based on a formula of Lascoux-Schutzenberger and its geometric interpretation by Zelevinsky. The first construction relies on a basis of the Hecke algebra constructed from principal lower order ideals in Bruhat order and a translation of this basis into sets of masks. The second construction relies on an interpretation of masks as cells of the Bott-Samelson resolution. These constructions give distinct answers to a question of Deodhar.

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