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Pré-Publication, Document De Travail Année : 2017

A proof of Lusztig's conjectures for affine type $G_2$ with arbitrary parameters

Résumé

We prove Lusztig's conjectures P1–P15 for the affine Weyl group of type˜G2type˜ type˜G2 for all choices of parameters. Our approach is based on the notion of a " balanced system of representations " for the Hecke algebra. Moreover we show that for arbitrary Coxeter type the existence of such a system is sufficient to compute Lusztig's a-function. We also describe connections between the cell decomposition and the structure of the Plancherel Theorem in type˜G2type˜ type˜G2.
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Dates et versions

hal-01638380 , version 1 (20-11-2017)
hal-01638380 , version 2 (12-12-2017)

Identifiants

  • HAL Id : hal-01638380 , version 1

Citer

Jeremie Guilhot, James Parkinson. A proof of Lusztig's conjectures for affine type $G_2$ with arbitrary parameters. 2017. ⟨hal-01638380v1⟩
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