3 problems

Let $O_q$ be the $q$-Onsager algebra, with alternating generators $\{W_{-i}\}_{i\in\mathbb N}$, $\{\tilde G_{j+1}\}_{j\in\mathbb N}$, and $\{W_{k+1}\}_{k\in\mathbb N}$. A linear or…

Let $\mathcal A_q$ be the current algebra over $\mathbb F$, with generators $\mathcal W_{-k}$, $\mathcal W_{k+1}$, $\mathcal G_{k+1}$, and $\mathcal{\tilde G}_{k+1}$ for…

PBW basis conjecture. These vectors induce a Poincare–Birkhoff–Witt-type basis of $\tilde{{\cal A}}_q^{\{\delta\}}$, called the $WG$-basis.