ﻻ يوجد ملخص باللغة العربية
We prove a character formula for the irreducible modules from the category $mathcal{O}$ over the simple affine vertex algebra of type $A_n$ and $C_n$ $(n geq 2)$ of level $k=-1$. We also give a conjectured character formula for types $D_4$, $E_6$, $E_7$, $E_8$ and levels $k=-1, cdots, -b$, where $b=2,3,4,6$ respectively.
In 2006, Gao and Zeng cite{GZ} gave the free field realizations of highest weight modules over a class of extended affine Lie algebras. In the present paper, applying the technique of localization to those free field realizations, we construct a clas
We construct a family of homomorphisms between Weyl modules for affine Lie algebras in characteristic p, which supports our conjecture on the strong linkage principle in this context. We also exhibit a large class of reducible Weyl modules beyond level one, for p not necessarily small.
The Bershadsky-Polyakov algebras are the minimal quantum hamiltonian reductions of the affine vertex algebras associated to $mathfrak{sl}_3$ and their simple quotients have a long history of applications in conformal field theory and string theory. T
We classify all simple bounded highest weight modules of a basic classical Lie superalgebra $mathfrak g$. In particular, our classification leads to the classification of the simple weight modules with finite weight multiplicities over all classical
Let $n>1$ be an integer, $alphain{mathbb C}^n$, $bin{mathbb C}$, and $V$ a $mathfrak{gl}_n$-module. We define a class of weight modules $F^alpha_{b}(V)$ over $sl_{n+1}$ using the restriction of modules of tensor fields over the Lie algebra of vector