On Lusztig's asymptotic Hecke algebra for ${\mathrm{SL}}_2$

Stefan Dawydiak

Let $H$ be the Iwahori-Hecke algebra and let $J$ be Lusztig's asymptotic Hecke algebra, both specialized to type ${\tilde{A}}_1$. For ${\mathrm{SL}}_2$, when the parameter $q$ is speci…