9 problems

Let $\Lambda_n$ index the cell modules $\Delta(\lambda)$ and simple modules $L(\mu)$ of the orientifold quiver Temperley--Lieb algebra, and let $\langle k\rangle$ denote grading sh…

Let $V^{(i)}_{k,q^p}$ denote the spectral shift of the Kirillov–Reshetikhin module $V^{(i)}_k$, and let $q^pK^{(i)}_k$ denote the corresponding grading shift of its generic kernel.…

Let $\mathfrak{O}(V^{(i)}_k,V^{(j)}_l)$ be the divisor of the normalized $R$-matrix denominator, and let $\dim_{q^{-1}}\mathop{\mathrm{ext}}^1_{\widetilde{\Pi}}$ denote the graded…

Let $\mathfrak{O}(M,N)$ be the divisor of the denominator of the normalized $R$-matrix between simple modules $M$ and $N$, and let…

Let $cmathcal{R}_{k,n}$ and $p_{calpha}$ be as in Section 2, with $d(calpha)$ denoting the degree of $p_{calpha}$. Let $cmathcal{H}_{k,n}$ be the graded space of $S_n$-harmonics th…

Let $\mathfrak{g}$ be a semisimple complex Lie algebra with Weyl group $W$, let $d,y\in W$ with $d$ a Duflo element, and let $\theta_d$ be the corresponding indecomposable projecti…

Let $\lambda,\mu\in\mathcal{P}^{l}_{n}$, $r\geq 0$, and $1\leq m\leq n$. Define…

Let $S^{\boldsymbol\mu}$ be a graded Specht module for a cyclotomic Hecke algebra of type $G(\ell,1,n)$, and let induction be taken from the corresponding Hecke algebra on $n$ lett…

Let $p$ be a prime. For a partition $\boldsymbol{\mu}=(\mu^{(1)},\dots,\mu^{(p-1)})\in M_{p-1}(d)$, let $w_H(\mu^{(p-1)})$ be the corresponding weight, and let the block of $p$-wei…