3 problems

For a function $L$ on the positive roots, define ${\mathrm{KL}}^{\mathfrak{g},L}_{\lambda,\mu}(q)$ by … For $L=L_A$, where $L_A(\alpha)=1$ for positive roots of type $A$ and…

Let $\tilde{\lambda}$ be the rectangular complement partition associated with $\lambda$ in $(g^n)$, and let $\tilde{\mu}$ be the corresponding complement for $\mu$. Let $T$ range o…

For a simple Lie algebra of type $C$, let ${\mathrm{KL}}^{C_n}_{\lambda,\mu}(q)$ denote Lusztig's $q$-weight multiplicity, and let the cyclage on Kashiwara–Nakajima tableaux define…