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arXiv · 2406.07004

The asymptotic Plancherel formula and Lusztig's asymptotic algebra for $\tilde{\mathsf{A}}_n$

Nathan Chapelier-Laget·Jérémie Guilhot·Eloise Little·James Parkinson
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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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Nathan Chapelier-Laget, Jérémie Guilhot, Eloise Little, James Parkinson. 2024-06-11. The asymptotic Plancherel formula and Lusztig's asymptotic algebra for $\tilde{\mathsf{A}}_n$. https://arxiv.org/abs/2406.07004

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