论文标题
$ qq $ - 字符的表示理论方法
A Representation-Theoretic Approach to $qq$-Characters
论文作者
论文摘要
我们提出了一个问题，即（略有概括的概念）$ qq $ - 字符可以从理论上纯粹构建代表。在量子环形$ \ mathfrak {gl} _1 $代数的主要示例中，伴随物质的几何工程产生一个显式的顶点操作员$ \ mathsf {rr} $，它计算某些$ qq $ - character $ \ mathsf {r} $ cumputes $ q $ -characters。我们给出了在此和更一般的非态度设置中首选方向的独立性的几何证明。
We raise the question of whether (a slightly generalized notion of) $qq$-characters can be constructed purely representation-theoretically. In the main example of the quantum toroidal $\mathfrak{gl}_1$ algebra, geometric engineering of adjoint matter produces an explicit vertex operator $\mathsf{RR}$ which computes certain $qq$-characters, namely Hirzebruch $χ_y$-genera, completely analogously to how the R-matrix $\mathsf{R}$ computes $q$-characters. We give a geometric proof of the independence of preferred direction for the refined vertex in this and more general non-toric settings.
