Balanced representations, the asymptotic Plancherel formula, and Lusztig's conjectures for C̃_2 [article]

J. Guilhot, J. Parkinson
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
more » ... e proof of Lusztig's conjectures for all rank 1 and 2 affine Weyl groups for all choices of parameters.
arXiv:1803.11067v2 fatcat:e4ads6ulwnadnk5f6jfhei4eka