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arXiv · 2206.04900

On the Unicity and the Ambiguity of Lusztig Parametrizations for Finite Classical Groups

Shu-Yen Pan
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Abstract

The Lusztig correspondence is a bijective mapping between the Lusztig series indexed by the conjugacy class of a semisimple element $s$ in the connected component $(G^*)^0$ of the dual group of $G$ and the set of irreducible unipotent characters of the centralizer of $s$ in $G^*$. In this article we discuss the unicity and ambiguity of such a bijective correspondence. In particular, we show that the Lusztig correspondence for a classical group can be made to be unique if we require it to be compatible with the parabolic induction and the finite theta correspondence.

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BibTeXRIS

Shu-Yen Pan. 2022-06-10. On the Unicity and the Ambiguity of Lusztig Parametrizations for Finite Classical Groups. https://arxiv.org/abs/2206.04900

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