论文标题
来自w-algebras的cosets
Cosets from equivariant W-algebras
论文作者
论文摘要
Equivariant $ \ MATHCAL {W} $ - 简单的Lie代数$ \ Mathfrak {G} $的代数是$ \ Mathfrak {g} $的Lie grout上手学差分运算符的代数。我们构建了一个顶点代数$ a [\ mathfrak {g}，κ，n] $作为$ \ m athfrak {g} $ a的$ \ mathcal {w} $ - algebra的sibergebras { langlands dual Lie代数$ \ check {\ Mathfrak {g}} $ at Level $ n \ in \ Mathbb {z} _ {> 0} $。它们是Aggine Vertex代数的张量产品和主要$ \ Mathcal {W} $ - 代数的保形扩展。
The equivariant $\mathcal{W}$-algebra of a simple Lie algebra $\mathfrak{g}$ is a BRST reduction of the algebra of chiral differential operators on the Lie group of $\mathfrak{g}$. We construct a family of vertex algebras $A[\mathfrak{g}, κ, n]$ as subalgebras of the equivariant $\mathcal{W}$-algebra of $\mathfrak{g}$ tensored with the integrable affine vertex algebra $L_n(\check{\mathfrak{g}})$ of the Langlands dual Lie algebra $\check{\mathfrak{g}}$ at level $n\in \mathbb{Z}_{>0}$. They are conformal extensions of the tensor product of an affine vertex algebra and the principal $\mathcal{W}$-algebra whose levels satisfy a specific relation.
