论文标题
Feigin-Semikhatov猜想和相关主题
Feigin-Semikhatov conjecture and related topics
论文作者
论文摘要
Feigin-Semikhatov现已建立的Feigin-Semikhatov指出，在亚规格的$ \ Mathcal {W} $ - 代数 - 代数和主要$ \ Mathcal {w} $ - A Type A类型的超级级别的Heisenberg Subergebras之间的代数同构。它可以看作是$ \ Mathcal {w} _n $ -Algebras之间的Feigin-Frenkel二元性的变体，也可以看作是$ \ Mathcal {n} = 2 $ superConformal代数与临时代数和仿率algebra $ \ hat {\ hat {\ naterfrak {在代数，模块和相互交织的操作员（包括融合规则）级别上，亚量级级别的W-Algebras和A型A型的主要W-Superalgebras的对应关系，包括融合规则。
Feigin-Semikhatov conjecture, now established, states algebraic isomorphisms between the cosets of the subregular $\mathcal{W}$-algebras and the principal $\mathcal{W}$-superalgebras of type A by their full Heisenberg subalgebras. It can be seen as a variant of Feigin-Frenkel duality between the $\mathcal{W}_n$-algebras and also as a generalization of the connection between the $\mathcal{N}=2$ superconformal algebra and the affine algebra $\hat{\mathfrak{sl}}_{2,k}$.We review the recent developments on the correspondence of the subregular W-algebras and the principal W-superalgebras of type A at the level of algebras, modules and intertwining operators, including fusion rules.
