10 problems

For a level $\ell$ and multipartition data $\mu,\nu$, let $\mathrm{ParMat}_{\nu,\mu}^{\flat}$ denote the corresponding set of enriched block matrices, let…

Let $\lambda$ be a partition with $n$ parts, and let $M=(m_{i,j})_{1\le i,j \le n}\in\mathcal{M}_\lambda$ be a minimal matrix of shape $\lambda$. A matrix is Hankel when its entrie…

For permutations $v,w\in S_n$, let $\operatorname{Q}(v)$ and $\operatorname{Q}(w)$ denote their recording tableaux under the Robinson–Schensted correspondence. The steady-state tim…

For a permutation $w\in S_n$, let $\operatorname{Q}(w)$ be its recording tableau under the Robinson–Schensted correspondence, and let $\widehat{Q}$ be the tableau … The steady-stat…

Let $\mathcal{L}$ be a directed landscape restricted to times in the interval $[0,1]$, and let $\mathcal{B}$ be a parabolic Airy line ensemble. Let $f$ be the function satisfying ……

Let $cmathfrak{M}$ be the set of multisegments, let $cLambda(cmathfrak{m})$ be the RSK-standard representation attached to $cmathfrak{m}cincmathfrak{M}$, and let $cmathcal{R}'$ be…

Let $cmathfrak{m}$ be a multisegment with RSK data … For each ladder $cmathfrak{l}_i$, let $Z(cmathfrak{l}_i)$ be its irreducible representation, and define representations recursi…

Let $\mathcal{M}$ be the set of multisegments. For a multisegment $cmathfrak{m}$, let $cLambda(cmathfrak{m})$ be its RSK-standard representation, let $Z(cmathfrak{m})$ be the corre…

Mirabolic Robinson–Schensted–Knuth conjecture. The Kazhdan–Lusztig cells of $\mathcal{R}_n(q)$ are related to the mirabolic Robinson–Schensted–Knuth correspondence.

Let $\mathbf{B}(\widetilde{U}_q(\mathfrak{gl}_{>0}))$ and $\mathbf{B}(\widetilde{U}_q(\mathfrak{gl}_\infty))_0$ carry the crystal structures of types $A_{+\infty}$ and $A_\infty$,…