3 problems

Feigin's conjecture. The map $\Phi(i_1,\ldots,i_N)$ is an embedding, and, for at least one special reduced decomposition of $w_0$, it extends to an isomorphism

Let $\mathcal{A}$ be a $\mathcal{k}$-algebra of dimension $r$, let $\sigma$ be a $\mathcal{k}$-linear automorphism of $\mathcal{A}$, and let $C_{\mathcal{k}}(\mu_d)$ denote the num…

Let $a$ be a weak composition, let $\mathbb S(a)$ be the associated skew diagram, and let ${\mathfrak K}_{\mathbb S(a)}$ be its skew polynomial. The skew-polynomial expansion conje…