8 problems

Gelfand–Tsetlin p-part conjecture. The $p$-part constructed from $f(\mathbf{x};\ell)$ should coincide with the $p$-part arising from the Gelfand–Tsetlin-pattern construction.

Let $\mu$ be a probability measure and let $[\mu]_\tau$ denote its free compression for $\tau\in[0,1]$. Define the sub-probability measure $\mu_\tau$ of total mass $\tau$ by…

Let $V_\lambda$ be the representation under consideration, let $\mathcal{A}^\mp$ denote the relevant limit shift-of-argument subalgebra, and let $z(t)$ be a path connecting $0$ to…

Let $V_\lambda$ be an irreducible finite-dimensional module for $\mathfrak{g}_n=\mathfrak{sp}_{2n}$ or $\mathfrak{o}_{2n+1}$. The eigenlines of the corresponding limit shift-of-arg…

Let $\mathfrak{g}_n$ be either $\mathfrak{sp}_{2n}$ or $\mathfrak{o}_{2n+1}$, let $V_\lambda$ be an irreducible finite-dimensional $\mathfrak{g}_n$-module, and let the eigenbasis o…

Fix partitions ${\lambda}/{\mu}$ and ${\nu}$. Let $\psi_k:GT_{k{\lambda}/k{\mu},k{\nu}}\to GT_{{\lambda}/{\mu},{\nu}}$ be the map sending a pattern to the unique lexicographically…

Fix partitions ${\lambda}/{\mu}$ and ${\nu}$, let $G\in GT_{{\lambda}/{\mu},{\nu}}$, and define … Here $GT_{{\lambda}/{\mu},{\nu}}$ is the set of relevant Gelfand–Tsetlin patterns…

Fix partitions ${\lambda}/{\mu}$ and ${\nu}$, let $G$ be an element of $GT_{{\lambda}/{\mu},{\nu}}$, and define … Here $GT_{{\lambda}/{\mu},{\nu}}$ denotes the set of Gelfand–Tsetl…