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arXiv · 2608.14879

Symplectic F_2-vector spaces and Dyck words

G. Lusztig
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Abstract

Let $V$ be an $F_2$-vector space with a given nondegenerate symplectic form and a circular basis. We define a partition of $V$ into subsets each of which has cardinal equal to a product of Catalan numbers. This can be viewed as a partition of the set of unipotent representations of a finite symplectic group corresponding to a certain two-sided cell.

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G. Lusztig. 2026-08-14. Symplectic F_2-vector spaces and Dyck words. https://arxiv.org/abs/2608.14879

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