Isocategorical groups and their Weil representations

Galindo, César

doi:10.1090/tran/6919

Isocategorical groups and their Weil representations
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by César Galindo PDF

Trans. Amer. Math. Soc. 369 (2017), 7935-7960 Request permission

Abstract:

Two groups are called isocategorical over a field $k$ if their respective categories of $k$-linear representations are monoidally equivalent. We classify isocategorical groups over arbitrary fields, extending the earlier classification of Etingof-Gelaki and Davydov for algebraically closed fields. In order to construct concrete examples of isocategorical groups a new variant of the Weil representation associated to isocategorical groups is defined. We construct examples of non-isomorphic isocategorical groups over any field of characteristic different from two and rational Weil representations associated to symplectic spaces over finite fields of characteristic two.

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