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

2022/06/10 by Shu-Yen Pan, Pan, Shu-Yen
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2206.04900

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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