14 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 $U(\tlie g)$ be the loop algebra enveloping algebra associated to a complex finite-dimensional simple Lie algebra, and let the corresponding quantum loop algebra have finite-di…

The paper considers Weyl modules for hyper loop algebras over an algebraically closed field of positive characteristic, together with their analogues obtained from characteristic-z…

Let $(X,G)$ be a datum consisting of a smooth projective curve and a finite group action with $X/G\simeq\mathbb{P}^1$, and let $\Psi$ be the homomorphism from the completed quantum…

Let $X$ be a smooth projective curve with a fixed group $G\subset\operatorname{Aut}(X)$ such that $X/G\simeq\mathbb{P}^1$, and let $\widehat{\mathfrak{U}}_{\mathbb{A}}$ be the comp…

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…

Consider a highest weight representation of the $sl_2$ loop algebra arising in the setting of the six-vertex model at roots of unity, and the Onsager algebra symmetry of the chiral…

Let $U$ be the enveloping algebra of the $sl_2$ loop algebra, and let $V$ be a finite-dimensional representation of this algebra. Deguchi's decomposition conjecture. Every finite-d…

Let $U$ be the enveloping algebra of the $sl_2$ loop algebra, and let $\rho$ be a finite-dimensional highest weight representation with a fixed highest weight. The paper describes…

Let $\mathfrak g=\bigoplus_{i=-d}^{\infty}\mathfrak g_i$ be a simple twisted loop superalgebra. An outer automorphism of $\mathfrak g$ is an automorphism modulo inner automorphisms…

Let $\fg$ be a simple Lie superalgebra, let $\Aut\fg$ be its group of all automorphisms, and let $\Int\fg$ be the subgroup of inner automorphisms. An outer automorphism is an eleme…

Let the spin-$1/2$ XXZ model be evaluated at a root-of-unity anisotropy, and let the Onsager algebra be regarded as a subalgebra of the $\mathfrak{sl}_{2}$ loop algebra. Onsager sy…