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The asymptotic Plancherel formula and Lusztig's asymptotic algebra for An

Nathan Chapelier
Jeremie Guilhot
Eloise Little
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Abstract

The aim of this paper is to give a new explicit construction of Lusztig's asymptotic algebra in affine type~$\mathsf{A}$. To do so, we construct a balanced system of cell modules, prove an asymptotic version of the Plancherel Theorem and develop a relative version of the Satake Isomorphism for each two-sided Kazhdan-Lusztig cell.
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Dates and versions

hal-04629409 , version 1 (29-06-2024)

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  • HAL Id : hal-04629409 , version 1

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Nathan Chapelier, Jeremie Guilhot, Eloise Little, James Parkinson. The asymptotic Plancherel formula and Lusztig's asymptotic algebra for An. 2024. ⟨hal-04629409⟩
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