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

2024/06/11 by Chapelier-Laget, Nathan, Guilhot, Jérémie, Little, Eloise +1
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2406.07004

Abstract

The aim of this paper is to give a new explicit construction of Lusztig's asymptotic algebra in affine type 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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