AFLT-type Selberg integrals

DOI10.1007/s00220-021-04157-0zbMath1483.33007arXiv2001.05637OpenAlexW2998930542WikidataQ114230935 ScholiaQ114230935MaRDI QIDQ2244915

Eric M. Rains, S. Ole Warnaar, Seamus P. Albion

Publication date: 12 November 2021

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.05637

zbMATH Keywords

Macdonald polynomialsJack polynomialsSelberg integralCauchy equalityelliptic interpolation polynomials

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Supersymmetric field theories in quantum mechanics (81T60) Yang-Mills and other gauge theories in quantum field theory (81T13) Other hypergeometric functions and integrals in several variables (33C70) (q)-gamma functions, (q)-beta functions and integrals (33D05) Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52)

Related Items

AGT basis in SCFT for c = 3/2 and Uglov polynomials, The AFLT \(q\)-Morris constant term identity, \(q\)-difference systems for the Jackson integral of symmetric Selberg type, An elliptic hypergeometric function approach to branching rules, A slow review of the AGT correspondence

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Elliptic Littlewood identities
• A Selberg integral for the Lie algebra \(A_n\)
• Cubic curves from instanton counting
• Whittaker vectors of the Virasoro algebra in terms of Jack symmetric polynomial
• On combinatorial expansion of the conformal blocks arising from AGT conjecture
• Proving AGT conjecture as HS duality: Extension to five dimensions
• Seiberg-Witten prepotential from instanton counting
• \(BC_n\)-symmetric abelian functions
• Correspondence between conformal field theory and Calogero-Sutherland model
• The \({\mathfrak{sl}}_3\) Selberg integral
• Transformations of elliptic hypergeometric integrals
• Limits of elliptic hypergeometric integrals
• Fock space representations of the Virasoro algebra. Intertwining operators
• \(BC\)-type interpolation Macdonald polynomials and binomial formula for Koornwinder polynomials
• A \(_1\Psi_1\) summation theorem for Macdonald polynomials
• Advanced determinant calculus
• Shifted Jack polynomials, binomial formula, and applications
• The Selberg-Jack symmetric functions
• Selberg-type integrals associated with \(\mathfrak{sl}_3\)
• Transformation formulas for multivariable basic hypergeometric series
• Toda 3-point functions from topological strings. II
• Some combinatorial properties of Jack symmetric functions
• Invariant skew-symmetric differential operators on the line and Verma modules over the Virasoro algebra
• Singular vectors of the Virasoro algebra in terms of Jack symmetric polynomials
• Trinion conformal blocks from topological strings
• Determinantal elliptic Selberg integrals
• Selberg integral and \(\mathrm{SU}(N)\) AGT conjecture
• Integrable structure, W-symmetry and AGT relation
• Liouville correlation functions from four-dimensional gauge theories
• Limits of elliptic hypergeometric biorthogonal functions
• Short proofs of the elliptic beta integrals
• 2d-4d connection between \(q\)-Virasoro/\(W\) block at root of unity limit and instanton partition function on ALE space
• On the generalised Selberg integral of Richards and Zheng
• \(q\)-Selberg integrals and Macdonald polynomials
• On the elliptic beta function
• LIOUVILLE FIELD THEORY: A DECADE AFTER THE REVOLUTION
• The importance of the Selberg integral
• Liouville theory revisited
• First order analytic difference equations and integrable quantum systems
• AN ALGORITHM FOR THE MICROSCOPIC EVALUATION OF THE COEFFICIENTS OF THE SEIBERG–WITTEN PREPOTENTIAL
• Hankel hyperdeterminants and Selberg integrals
• $q$-Selberg integrals and Macdonald polynomials
• Bounded Littlewood identities
• Evaluation of the $BC_n$ elliptic Selberg integral via the fundamental invariants
• An elliptic Macdonald-Morris conjecture and multiple modular hypergeometric sums