6 problems

Let $K$ be a field of characteristic zero, let $q$ be a nonzero element of $K$ that is not a root of unity, and let $\mathcal{O}_{q}(G(k,n))$ be the quantum grassmannian with…

Braid-group preservation conjecture. The maps $\sigma_i$ and $\sigma_i^{-1}$ also preserve $r$-term quantum Plücker relations for $r\geq 4$ in…

Let ${\mathcal H}$ act on the quantum Grassmannian ${\cal O}_q(G_{mn}({\mathbb K}))$. For an ${\mathcal H}$-prime ideal, consider the quantum Plücker coordinates it contains; the P…

Let $G_{mn}^{ 0}( R)$ be the totally nonnegative Grassmannian, stratified by positroid cells, and let ${ H}\!\operatorname{-Spec}({\cal O}_q(G_{mn}({\mathbb K})))$ be the partially…

Let ${\mathbb C}_q[\operatorname{Gr}_{n,r}]$ be the coordinate algebra of a quantum Grassmannian, equipped with its Heckenberger–Kolb differential calculus and its anti-holomorphic…

Let $q$ be not a root of unity, and let ${\mathcal H}$ be the algebraic torus acting on the quantum Grassmannian $\mathcal{O}_{q}(G(m,n))$ through its natural ${\mathbb Z}^n$-gradi…