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Balanced representations, the asymptotic Plancherel formula, and Lusztig's conjectures for C̃_2
[article]
2018
arXiv
pre-print
We prove Lusztig's conjectures P1- P15 for the affine Weyl group of type C̃_2 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 C̃_2, from which the remaining conjectures follow. Combined with existing results in the literature this completes
arXiv:1803.11067v2
fatcat:e4ads6ulwnadnk5f6jfhei4eka