Balanced representations, the asymptotic Plancherel formula, and Lusztig's conjectures for C₂

2018/03/27 by Jérémie Guilhot, Guilhot, J., James Parkinson +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Graph theory and applications #Random Matrices and Applications #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1803.11067

openalex publication_date 2018/03/27 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

We prove Lusztig's conjectures \bf P1-\bf P15 for the affine Weyl group of type C₂ for all choices of positive weight function. Our approach to computing Lusztig's a-function is based on the notion of a `balanced system of cell representations'. Once this system is established roughly half of the conjectures \bf P1-\bf P15 follow. Next we establish an `asymptotic Plancherel Theorem' for type C₂, from which the remaining conjectures follow. Combined with existing results in the literature this completes the proof of Lusztig's conjectures for all rank 1 and 2 affine Weyl groups for all choices of parameters.

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