qq字符的表示理论方法

IF 0.9 3区 物理与天体物理 Q2 MATHEMATICS
Henry Liu
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引用次数: 1

摘要

我们提出了一个问题,即$qq$-字符(一个稍微广义的概念)是否可以在理论上被构造为纯粹的表示。在量子超环面$\mathfrak的主要例子中{gl}_1$代数,伴随物质的几何工程产生了一个显式顶点算子$\mathsf{RR}$,它计算某些$qq$-字符,即Hirzebruch$\chi_y$-属,完全类似于R-矩阵$\mathsf{R}$计算$q$-字符的方式。在这个和更一般的非复曲面设置中,我们给出了精化顶点的优选方向独立性的几何证明。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Representation-Theoretic Approach to qq-Characters
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 $\chi_y$-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.
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来源期刊
CiteScore
1.80
自引率
0.00%
发文量
87
审稿时长
4-8 weeks
期刊介绍: Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.
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