Year: 2025
Type: preprint
Abstract: This is an extended abstract of our work "Level-Rank Dualities from $Φ$-Cuspidal Pairs..." We present evidence for a family of surprising coincidences within the representation theory of a finite reductive group $G$: more precisely, dualities between blocks of cyclotomic Hecke algebras attached by Broué-Malle to $Φ$-cuspidal pairs of $G$, where the Hecke parameters are specialized not to the order of the underlying finite field, but to roots of unity. For the groups $G = \mathrm{GL}_n(\mathbf{F}_q)$, these coincidences can be expressed very concretely in terms of the combinatorics of partitions, and the whole story recovers an avatar of the level-rank duality studied by Frenkel, Uglov, Chuang-Miyachi, and others.
Source: arXiv (Cornell University)
Authors: Trinh, Minh-Tâm Quang, Xue, Ting
Institution: Howard University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416182278
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