5 problems

Let $W$ be a Weyl group, let $\rho_k$ denote the associated weighted half-sum, let $l$ be the shift parameter, and let $S(\mathfrak{h})$ be the symmetric algebra of the Cartan spac…

Okounkov's shift-operator R-matrix conjecture. In the stable basis, the operator $S_\mathsf{w}$ is conjugate to the R-matrix for

Okounkov's shift-operator conjecture. In the stable basis, the operator $S_\mathsf{w}$ is conjugate to

Let $\ell_2({\mathbb Z}_+)$ be the complex Hilbert space of square-summable sequences indexed by $\mathbb Z_+$, and let $B^*$ be the backward shift on this space. Feldman's conject…

Let $\mathbf m=\bigl(\lambda_{j,\nu}\bigr)_{\substack{0\le j\le p\\1\le\nu\le n_j}}\in\mathcal P^{(n)}_{p+1}$ be a rigid tuple of partitions, and let…