Quantum Representation of Affine Weyl Groups and Associated Quantum Curves

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2021
• Main Authors: Moriyama, Sanefumi, Yamada, Yasuhiko
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2021
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211347
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Quantum Representation of Affine Weyl Groups and Associated Quantum Curves. Sanefumi Moriyama and Yasuhiko Yamada. SIGMA 17 (2021), 076, 24 pages

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''...