4 problems

Let $\Gamma$ be a $Q$-polynomial distance-regular graph with eigenvalues $\theta_i$ and dual eigenvalues $\theta_i^*$. For $2\leq i\leq D-1$, define … Assume these expressions are equ…

Let $\Gamma$ be a distance-regular graph with classical parameters $(D,b,\alpha,\beta)$, where $b\ne1$, and suppose $\Gamma$ is not a dual polar graph. Let $T$ be its Terwilliger alg…

Let $V$ be a finite-dimensional irreducible $\boxtimes_q$-module of type $1$, and let $\omega$ be the antiautomorphism of $\boxtimes_q$ from Lemma. Invariant-form conjecture. There…

Let ${\mathcal A}_q$ be the unital associative algebra generated by $x,y$ subject to the two cubic $q$-Serre relations … … For each $i\in\mathbb Z_4$, let the homomorphism from…