Non-Stationary Difference Equation and Affine Laumon Space II: Quantum Knizhnik-Zamolodchikov Equation

• Опубліковано в: : Symmetry, Integrability and Geometry: Methods and Applications
• Дата: 2024
• Автори: Awata, Hidetoshi, Hasegawa, Koji, Kanno, Hiroaki, Ohkawa, Ryo, Shakirov, Shamil, Shiraishi, Jun'ichi, Yamada, Yasuhiko
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Інститут математики НАН України 2024
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/212343
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: Non-Stationary Difference Equation and Affine Laumon Space II: Quantum Knizhnik-Zamolodchikov Equation. Hidetoshi Awata, Koji Hasegawa, Hiroaki Kanno, Ryo Ohkawa, Shamil Shakirov, Jun'ichi Shiraishi and Yasuhiko Yamada. SIGMA 20 (2024), 077, 55 pages

We show that Shakirov's non-stationary difference equation, when it is truncated, implies the quantum Knizhnik-Zamolodchikov (-KZ) equation for ᵥ(⁽¹⁾₁) with generic spins. Namely, we can tune mass parameters so that the Hamiltonian acts on the space of finite Laurent polynomials. Then the representation matrix of the Hamiltonian agrees with the -matrix, or the quantum 6 symbols. On the other hand, we prove that the K-theoretic Nekrasov partition function from the affine Laumon space is identified with the well-studied Jackson integral solution to the -KZ equation. Combining these results, we establish that the affine Laumon partition function gives a solution to Shakirov's equation, which was a conjecture in our previous paper. We also work out the base-fiber duality and four-dimensional limit in relation to the -KZ equation.