A footnote to a paper of Deodhar

Davide Franco

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arXiv · 2308.01585

A footnote to a paper of Deodhar

Davide Franco

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Abstract

Let $X\subseteq G\slash B$ be a Schubert variety in a flag manifold and let $\pi: \tilde X \rightarrow X$ be a Bott-Samelson resolution of $X$. In this paper we prove an effective version of the decomposition theorem for the derived pushforward $R \pi_{*} \mathbb{Q}_{\tilde{X}}$. As a by-product, we obtain recursive procedure to extract Kazhdan-Lusztig polynomials from the polynomials introduced by V. Deodhar in \cite{Deo}, which does not require prior knowledge of a minimal set. We also observe that any family of equivariant resolutions of Schubert varieties allows to define a new basis in the Hecke algebra and we show a way to compute the transition matrix, from the Kazhdan-Lusztig basis to the new one.

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Davide Franco. 2023-08-03. A footnote to a paper of Deodhar. https://arxiv.org/abs/2308.01585

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