Existence and Orthogonality of Generalized Jack Polynomials and Its $q$-Deformation

Abstract

We investigate the existence and the orthogonality of the generalized Jack symmetric functions which play an important role in the AGT relations. We show their orthogonality by deforming them to the generalized Macdonald symmetric functions.

6 pages

References in corpus (5)

• A direct proof of AGT conjecture at beta = 1
• Finalizing the proof of AGT relations with the help of the generalized Jack polynomials
• Generalized Jack polynomials and the AGT relations for the $SU(3)$ group
• Generalized Macdonald polynomials, spectral duality for conformal blocks and AGT correspondence in five dimensions
• An M-Theoretic Derivation of a 5d and 6d AGT Correspondence, and Relativistic and Elliptized Integrable Systems

Cited by in corpus (6)

• A slow review of the AGT correspondence
• Crystallization of deformed Virasoro algebra, Ding-Iohara-Miki algebra and 5D AGT correspondence
• On generalized Macdonald polynomials
• Refined toric branes, surface operators and factorization of generalized Macdonald polynomials
• Non-Stationary Ruijsenaars Functions for $\kappa =t^{-1/N}$ and Intertwining Operators of Ding-Iohara-Miki Algebra
• Free field approach to the Macdonald process