论文标题
$ \ MATHCAL W $代数的变形通过量子图代数
Deformations of $\mathcal W$ algebras via quantum toroidal algebras
论文作者
论文摘要
类型$ \ textsf {a} $的变形$ \ Mathcal W $代数在量子图形$ \ mathfrak {gl} _1 $ algebra $ \ mathcal e $方面具有统一描述。我们在$ \ Mathcal e $上引入了一个Comodule代数$ \ Mathcal K $，该$ \ Mathcal e $均在类型的$ \ textsf {b}，\ textsf {c}，\ textsf {c}，\ textsf {d} $中均构成基本变形$ \ Mathcal w $电流和筛选操作员。我们表明，代数$ \ Mathcal k $的完成包含三个换向的亚代词。特别是，它允许我们获得与所有非视类型类型的仿射dynkin图相关联的运动积分家族，但$ \ textsf {d}^{（2）} _ {\ ell+1} $。我们还以统一的方式在所有经典类型中以及许多新示例中以统一的变形有限和仿射卡坦矩阵获得，并讨论相应的筛选算子。
The deformed $\mathcal W$ algebras of type $\textsf{A}$ have a uniform description in terms of the quantum toroidal $\mathfrak{gl}_1$ algebra $\mathcal E$. We introduce a comodule algebra $\mathcal K$ over $\mathcal E$ which gives a uniform construction of basic deformed $\mathcal W$ currents and screening operators in types $\textsf{B},\textsf{C},\textsf{D}$ including twisted and supersymmetric cases. We show that a completion of algebra $\mathcal K$ contains three commutative subalgebras. In particular, it allows us to obtain a commutative family of integrals of motion associated with affine Dynkin diagrams of all non-exceptional types except $\textsf{D}^{(2)}_{\ell+1}$. We also obtain in a uniform way deformed finite and affine Cartan matrices in all classical types together with a number of new examples, and discuss the corresponding screening operators.
