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The asymptotic Plancherel formula and Lusztig's asymptotic algebra for $\tilde{\mathsf{A}}_n$
Published 11 Jun 2024 in math.RT | (2406.07004v2)
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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