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## Mask formulas for cograssmannian Kazhdan-Lusztig polynomials

- Author(s): Jones, Brant
- Woo, Alexander
- et al.

## Published Web Location

https://arxiv.org/pdf/1011.1110.pdfNo data is associated with this publication.

## Abstract

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.