Kac determinant and singular vector of the level N representation of Ding-Iohara-Miki algebra

Abstract

In this paper, we obtain the formula for the Kac determinant of the algebra arising from the level $N$ representation of the Ding-Iohara-Miki algebra. It is also discovered that its singular vectors correspond to generalized Macdonald functions (the q-deformed version of the AFLT basis).

Based on Chapter 3 in arXiv:1703.10990. Theorem 4.4 is generalized. 24 pages, 3 figures

References in corpus (8)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Notes on Ding-Iohara algebra and AGT conjecture
• Finite type modules and Bethe Ansatz for quantum toroidal gl(1)
• Toric Calabi-Yau threefolds as quantum integrable systems. R-matrix and RTT relations
• Anomaly in RTT relation for DIM algebra and network matrix models
• Kernel function and quantum algebras
• Quantum toroidal gl(1) and Bethe ansatz
• Maulik-Okounkov's R-matrix from Ding-Iohara-Miki algebra

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• A slow review of the AGT correspondence
• Generalized Macdonald Functions on Fock Tensor Spaces and Duality Formula for Changing Preferred Direction
• Non-Stationary Ruijsenaars Functions for $\kappa =t^{-1/N}$ and Intertwining Operators of Ding-Iohara-Miki Algebra
• Symmetric functions in superspace: a compendium of results and open problems (including a SageMath worksheet)
• Direct Sum Structure of the Super Virasoro Algebra and a Fermion Algebra Arising from the Quantum Toroidal ${\mathfrak{gl}}_2$