A pinned canonical bijection is constructed between Lusztig series and unipotent characters of possibly disconnected dual centralizers for finite reductive groups, with an enriched version for disconnected groups.
arXiv preprint arXiv:2408.07805 , year=
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J(G) for inner forms G of p-adic GL_n is defined over ar Q_l, admits explicit formulas via reductive centralizers, shares Hochschild homology with C_c^infty(G), and supports rudimentary Hecke compatibility for sheaves on Bun_n.
citing papers explorer
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Pinned Jordan Decomposition of Characters and Depth-Zero Hecke Algebras
A pinned canonical bijection is constructed between Lusztig series and unipotent characters of possibly disconnected dual centralizers for finite reductive groups, with an enriched version for disconnected groups.
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On Braverman-Kazhdan's asymptotic Hecke algebra for inner forms of $\mathrm{GL}_n$
J(G) for inner forms G of p-adic GL_n is defined over ar Q_l, admits explicit formulas via reductive centralizers, shares Hochschild homology with C_c^infty(G), and supports rudimentary Hecke compatibility for sheaves on Bun_n.