Norm of the Whittaker vector of the deformed Virasoro algebra

Abstract

We give a proof of the recursive formula on the norm of Whittaker vector of the deformed Virasoro algebra, which is an analog of the one for the Virasoro Lie algebra proposed by Al. Zamolodchikov. Our formula gives a proof of the pure SU(2) 5d AGT relation proposed by Awata and Yamada. We also give a summary of the structures of the deformed Virasoro algebra and the fundamental properties of the Verma module.

References in corpus (7)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Five-dimensional AGT Conjecture and the Deformed Virasoro Algebra
• Asymptotically free N=2 theories and irregular conformal blocks
• On AGT conjecture
• Instanton moduli spaces and $\mathcal{W}$-algebras
• The deformed Virasoro algebra at roots of unity
• Algebraic integrability of Schrödinger operators and representations of Lie algebras

Cited by in corpus (5)

• Cluster integrable systems, q-Painleve equations and their quantization
• Analyticity of Nekrasov Partition Functions
• Crystallization of deformed Virasoro algebra, Ding-Iohara-Miki algebra and 5D AGT correspondence
• Combinatorial expressions for the tau functions of $q$-Painlevé V and III equations
• Singular Vector of Ding-Iohara-Miki Algebra and Hall-Littlewood Limit of 5D AGT Conjecture