3 problems

Let $X$ be a two-sided Hecke pattern of rank $r$. Write $H_*(X)$ for its Borel–Moore homology, and let $W_{\star,\star}(S)$ denote the algebra with the appropriate choices of indic…

Isomorphism conjecture. The three algebras are isomorphic as associative algebras:

Let ${\cal I}_n$, for $n=1,2,\ldots$, be the Local Integrals of Motion for the deformed $W$-algebra $W_{q,t}(\widehat{sl_N})$, defined by analytic continuation when necessary. Let…