Symmetry Integrability and Geometry-Methods and Applications | |
A Representation-Theoretic Approach to $qq$-Characters | |
article | |
Henry Liu1  | |
[1] Mathematical Institute, University of Oxford | |
关键词: $qq$-characters; geometric engineering; vertex operators; R-matrices; Pandharipande-Thomas theory.; | |
DOI : 10.3842/SIGMA.2022.090 | |
来源: National Academy of Science of Ukraine | |
【 摘 要 】
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.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
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RO202307120000523ZK.pdf | 623KB | download |