7 problems

Let $L$ be a finite-dimensional simple module over the relevant KLR algebra, let $d_L$ be the corresponding vector in the dual canonical basis of ${\mathbb C}[N]$, and let $b_Z$ be…

MV-basis cluster conjecture. The MV basis for $\mathbb C[N]$ contains all cluster monomials. Moreover, every element of the MV basis is $g$-pointed in each cluster.

Module-structure conjecture. For every preprojective algebra module $M$ of dimension vector $\nu$, the direct sum

Let $M$ be a module for a preprojective algebra, and let $\mathbb G(M[t]/t^n)$ denote the variety of submodules of the preprojective algebra module obtained by tensoring $M$ with…

Let $G$ be the group in the affine-Grassmannian setup, let $\lambda\in P_+$, let $t^{-\lambda}\overline{{\rm Gr}^{\lambda}}$ be the shifted spherical Schubert variety, and let…

For a complex semisimple algebraic group, consider the generalizations of the Young-tableaux and MV-cycle results described above, formulated in terms of the plactic algebra define…

The construction associates Bott–Samelson-type varieties and Białynicki-Birula cells to galleries, with the images of cells associated to Knuth-equivalent galleries sharing a commo…