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.
Acknowledgments
The author would like to thank the referee for his/her careful reading and several very useful suggestions. In particular, the author appreciates the referee's help very much for pointing out a few errors in the first version of the article.
Citation
Shu-Yen Pan. "On the Unicity and the Ambiguity of Lusztig Parametrizations for Finite Classical Groups." Taiwanese J. Math. 28 (3) 423 - 473, June, 2024. https://doi.org/10.11650/tjm/240103
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