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arXiv · 1711.06462

Association schemes on the Schubert cells of a Grassmannian

Yuta Watanabe
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Abstract

Let $\mathbb{F}$ be any field. The Grassmannian $\mathrm{Gr}(m,n)$ is the set of $m$-dimensional subspaces in $\mathbb{F}^n$, and the general linear group $\mathrm{GL}_n(\mathbb{F})$ acts transitively on it. The Schubert cells of $\mathrm{Gr}(m,n)$ are the orbits of the Borel subgroup $\mathcal{B} \subset \mathrm{GL}_n(\mathbb{F})$ on $\mathrm{Gr}(m,n)$. We consider the association scheme on each Schubert cell defined by the $\mathcal{B}$-action and show it is symmetric and it is the generalized wreath product of one-class association schemes, which was introduced by R. A. Bailey [European Journal of Combinatorics 27 (2006) 428--435].

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Yuta Watanabe. 2017-11-17. Association schemes on the Schubert cells of a Grassmannian. https://arxiv.org/abs/1711.06462

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