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

J. Guilhot, J. Parkinson

We prove Lusztig's conjectures $P1$--$P15$ for the affine Weyl group of type ${\tilde{G}}_2$ for all choices of parameters. Our approach to compute Lusztig's $\mathbf{a}$…