Graded sum formula for ${\tilde{A}}_1$-Soergel calculus and the nil-blob algebra

Marcelo Hernández Caro, Steen Ryom-Hansen

We study the representation theory of the Soergel calculus algebra $ A_w := \mbox{End}_{{\mathcal D}_{(W,S)}} (\underline{w}) $ over $\mathbb{C}$ in type ${\tilde{A}}_1$. We generaliz…