论文标题
部分可观测时空混沌系统的无模型预测
Duality via convolution of W-algebras
论文作者
论文摘要
Feigin-Frenkel二重性是主要$ \ Mathcal {w} $ - 简单的lie代数$ \ mathfrak {g} $的代数与其langlands dual lie elgebra algebra $ {}^l \ mathfrak {g} $之间的同构。 Gaiotto和Rapčák最近猜想了这种双重性对$ \ Mathcal {W} $ - 代数为hook-type的代数的概括，并由前两位作者证明。它说，两个不同的钩型$ \ mathcal {w} $的仿射库 - 代数是同构的。一个自然的问题是，是否可以增强仿射库之间的双重性，从而在整个$ \ MATHCAL {W} $ - 代数之间具有双重性。有一个卷积操作将挂钩型$ \ Mathcal {w} $ - 代数$ \ Mathcal {W} $映射到$ \ Mathcal {W} $ a intersored的特定相对半偶然的同胞，并使用合适的kernel voa进行。前两位作者以前猜想这种同胞对Feigin-Frenkel双钩型$ \ Mathcal {W} $ - 代数 - 代数是同构。我们的主要结果是证明了这种猜想。
Feigin-Frenkel duality is the isomorphism between the principal $\mathcal{W}$-algebras of a simple Lie algebra $\mathfrak{g}$ and its Langlands dual Lie algebra ${}^L\mathfrak{g}$. A generalization of this duality to a larger family of $\mathcal{W}$-algebras called hook-type was recently conjectured by Gaiotto and Rapčák and proved by the first two authors. It says that the affine cosets of two different hook-type $\mathcal{W}$-algebras are isomorphic. A natural question is whether the duality between affine cosets can be enhanced to a duality between the full $\mathcal{W}$-algebras. There is a convolution operation that maps a hook-type $\mathcal{W}$-algebra $\mathcal{W}$ to a certain relative semi-infinite cohomology of $\mathcal{W}$ tensored with a suitable kernel VOA. The first two authors conjectured previously that this cohomology is isomorphic to the Feigin-Frenkel dual hook-type $\mathcal{W}$-algebra. Our main result is a proof of this conjecture.
