\(t,q\)-deformed \(Q\)-systems, DAHA and quantum toroidal algebras via generalized Macdonald operators

DOI10.1007/s00220-019-03472-xzbMath1464.17017OpenAlexW2605164526MaRDI QIDQ2311916

Philippe Di Francesco, Rinat Kedem

Publication date: 4 July 2019

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

Full work available at URL: https://doi.org/10.1007/s00220-019-03472-x

zbMATH Keywords

Macdonald polynomialsQ-systemdouble affine Hecke algebraquantum toroidal algebra

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Hecke algebras and their representations (20C08) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50)

Related Items

Multiplicative quiver varieties and generalised Ruijsenaars-Schneider models, SUSY localization for Coulomb branch operators in omega-deformed 3d \(\mathcal{N} = 4\) gauge theories, Weight-finite modules over the quantum affine and double quantum affine algebras of type \(\mathfrak{a}_1\), Difference operators via GKLO-type homomorphisms: shuffle approach and application to quantum \(Q\)-systems, Macdonald duality and the proof of the quantum Q-system conjecture, Quantum Q systems: from cluster algebras to quantum current algebras, Difference equations for graded characters from quantum cluster algebra, The \(R\)-matrix of the quantum toroidal algebra \(U_{q,t}(\overset{..}{gl}_1)\) in the Fock module, DAHA and skein algebra of surfaces: double-torus knots, Macdonald operators and quantum Q-systems for classical types, Quiver Yangian and supersymmetric quantum mechanics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some remarkable new plethystic operators in the theory of Macdonald polynomials
• On the Hall algebra of an elliptic curve. I.
• Quantum Q systems: from cluster algebras to quantum current algebras
• Non-commutative integrability, paths and quasi-determinants
• Drinfeld realization of the elliptic Hall algebra
• Seiberg-Witten prepotential from instanton counting
• Determinants and alternating sign matrices
• Eisenstein series and quantum affine algebras
• Generalization of Drinfeld quantum affine algebras
• Liouville correlation functions from four-dimensional gauge theories
• Fermionic sum representations for conformal field theory characters
• Rogers-Ramanujan type identities and nil-DAHA
• Quantum cluster algebras.
• Quantum Cluster Algebras and Fusion Products
• The Shuffle Algebra Revisited
• The elliptic Hall algebra, Cherednik Hecke algebras and Macdonald polynomials
• Q-systems as cluster algebras
• Proof of the Combinatorial Kirillov-Reshetikhin Conjecture
• A (q,γ) analog of the W1+∞ algebra
• A commutative algebra on degenerate CP1 and Macdonald polynomials