Quantum Representation of Affine Weyl Groups and Associated Quantum Curves
We study a quantum (non-commutative) representation of the affine Weyl group, primarily of type ⁽¹⁾₈, where the representation is given by birational actions on two variables, and , with q-commutation relations. Using the tau variables, we also construct quantum ''fundamental''...
Збережено в:
| Опубліковано в: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2021 |
| ISSN: | 1815-0659 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2021
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211347 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Quantum Representation of Affine Weyl Groups and Associated Quantum Curves. Sanefumi Moriyama and Yasuhiko Yamada. SIGMA 17 (2021), 076, 24 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | We study a quantum (non-commutative) representation of the affine Weyl group, primarily of type ⁽¹⁾₈, where the representation is given by birational actions on two variables, and , with q-commutation relations. Using the tau variables, we also construct quantum ''fundamental'' polynomials (, ) which completely control the Weyl group actions. The geometric properties of the polynomials (, ) for the commutative case are lifted distinctively in the quantum case to certain singularity structures as the q-difference operators. This property is further utilized as the characterization of the quantum polynomials (, ). As an application, the quantum curve associated with topological strings proposed recently by the first-named author is rederived by the Weyl group symmetry. The cases of type ⁽¹⁾₅, ⁽¹⁾₆, ⁽¹⁾₇ are also discussed.
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| ISSN: | 1815-0659 |