4 problems

Let $\mathbb F$ be an algebraically closed field of positive characteristic, let $\mathbb A$ be the coefficient ring used for reduction modulo the characteristic, and let…

Let $\mathbf{U}^+$ be the $\mathbb{C}_v$-subalgebra of $\mathbf{U}_v(L\mathfrak{gl}_p)$ generated by $\mathbf{U}_0^+$ and $h_{0,l}$ for $l>0$, where $\mathbf{U}_0^+$ is generated b…

Let $\Omega$ be a highest weight vector, let $m_j$ be the multiplicity associated with the parameter $a_j$, and let $w_{j^k}(\boldsymbol{\hat a})$ be the operators defined in the a…

Deguchi's highest-weight-vector conjecture. Every irreducible quotient of a submodule in $U\Omega$ has a highest weight vector of the form…