6 problems

Let $V_\ell$ denote the $U_q(gl_2(\mathbb{C}))$-module indexed by $\ell\geq 0$, and let $S_\sigma^n V_\ell$ be its $n$th braided symmetric power. Higher braided symmetric powers co…

Let $W$ be a Weyl group, let ${\cal C}$ be its set of reflections, and let $\Lambda_w$ be the left-invariant differential algebra associated with this differential structure. Let…

Let ${\cal N}$ be the algebra equipped with the braided differential operators defined by the matrix $D$, and let $Z({\cal N})$ denote its center. For each positive integer $k$, de…

Let $\mathcal{H}$ be the Hilbert space underlying a Wick algebra, let $T$ be a braided operator on $\mathcal{H}^{\mathcal{\otimes}2}$, and let $R_m$ denote the corresponding Wick sy…

Let $\mathfrak{g}$ be a simple Lie algebra, let $V^q$ be a simple $U_q(\mathfrak{g})$-module, and let $V$ be its classical limit. The degree-three braided symmetric and exterior po…

Let $\mathfrak{g}$ be a reductive Lie algebra, let $V^q$ be a finite-dimensional $U_q(\mathfrak{g})$-module, and let $V$ be its classical limit. The reduced symmetric algebra is…