A Representation-Theoretic Approach to -Characters
We raise the question of whether (a slightly generalized notion of) -characters can be constructed purely representation-theoretically. In the main example of the quantum toroidal ₁ algebra, geometric engineering of adjoint matter produces an explicit vertex operator which computes certain -cha...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2022 |
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| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2022
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211814 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | A Representation-Theoretic Approach to -Characters. Henry Liu. SIGMA 18 (2022), 090, 20 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | We raise the question of whether (a slightly generalized notion of) -characters can be constructed purely representation-theoretically. In the main example of the quantum toroidal ₁ algebra, geometric engineering of adjoint matter produces an explicit vertex operator which computes certain -characters, namely Hirzebruch χy-genera, completely analogously to how the -matrix computes -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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| ISSN: | 1815-0659 |