3 problems

Let $C$ be a triangular right coideal subalgebra of the form … Here $w_+,w_-\in W$, $\phi_+$ and $\phi_-$ are characters, $L$ is the associated lattice, $S$ is the antipode, and…

Let $W$ be the Weyl group, let $w\in W$, and let $\phi$ be a character. Give $U^-_q(\mathfrak{g})$ the $\mathbb{Z}$-grading determined by $\deg(E_{\alpha_i})=1$,…

Heckenberger–Vocke conjecture. The map $f$ is an injective homomorphism of $\mathbb{Z}$-graded right coideal subalgebras, and