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A proof of Lusztig's conjectures for affine type G2 with arbitrary parameters

A proof of Lusztig's conjectures for affine type G2 with arbitrary parameters

We prove Lusztig's conjectures P 1 ā€“ P 15 for the affine Weyl group of type G āˆ¼ 2 for all choices of parameters. Our approach to compute Lusztig's a-function is based on the notion of a ā€˜balanced system of cell representationsā€™ for the Hecke algebra. We show that for ā€¦