Balanced representations, the asymptotic Plancherel formula, and Lusztig's conjectures for C2 - Archive ouverte HAL Access content directly
Journal Articles Algebraic Combinatorics Year : 2019

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

Jérémie Guilhot

Abstract

We prove Lusztig's conjectures P1–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 P1–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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Dates and versions

hal-01745431 , version 1 (28-03-2018)

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Jérémie Guilhot, James Parkinson. Balanced representations, the asymptotic Plancherel formula, and Lusztig's conjectures for C2. Algebraic Combinatorics, 2019, 2 (5), pp.969-1031. ⟨10.5802/alco.75⟩. ⟨hal-01745431⟩
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