The \(R\)-matrix of the quantum toroidal algebra \(U_{q,t}(\overset{..}{gl}_1)\) in the Fock module

DOI10.1007/s00220-021-04023-zzbMath1476.17006arXiv2004.09241OpenAlexW3132022588MaRDI QIDQ2031137

Alexandr Garbali, Jan De Gier

Publication date: 8 June 2021

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

Full work available at URL: https://arxiv.org/abs/2004.09241

zbMATH Keywords

R-matrixHopf algebras and their applicationsFock modulesquantum groups and related algebraic methodsbasic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.)rings determined by universal properties

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Groups and algebras in quantum theory and relations with integrable systems (81R12) Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52) Ring-theoretic aspects of quantum groups (16T20)

Related Items (6)

Computing the R-matrix of the quantum toroidal algebra ⋮ Quantum toroidal comodule algebra of type \(A_{n-1}\) and integrals of motion ⋮ The \(R\)-matrix of the quantum toroidal algebra ⋮ Gauge/Bethe correspondence from quiver BPS algebras ⋮ Quasi-Hopf twist and elliptic Nekrasov factor ⋮ Shifted quiver quantum toroidal algebra and subcrystal representations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the instanton \(R\)-matrix
• Some remarkable new plethystic operators in the theory of Macdonald polynomials
• Cherednik algebras, \(W\)-algebras and the equivariant cohomology of the moduli space of instantons on \(\mathbb A^2\)
• On the Hall algebra of an elliptic curve. I.
• Quantum toroidal \(\mathfrak{gl}_{1}\)-algebra: plane partitions
• Anomaly in \(\mathcal{RTT}\) relation for DIM algebra and network matrix models
• Branching rules for symmetric functions and \(\mathfrak{sl}_n\) basic hypergeometric series
• Quantum continuous \(\mathfrak{gl}_{\infty}\): semiinfinite construction of representations
• Equivariant \(K\)-theory of Hilbert schemes via shuffle algebra
• Quantum toroidal and shuffle algebras
• A family of integral transformations and basic hypergeometric series
• Quantum inverse problem method. I
• Toric Calabi-Yau threefolds as quantum integrable systems. \(\mathcal R\)-matrix and \(\mathcal{RTT}\) relations
• The \(q\)-AGT-W relations via shuffle algebras
• Langlands reciprocity for algebraic surfaces
• The elliptic Hall algebra and the \(K\)-theory of the Hilbert scheme of \(\mathbb{A}^{2}\)
• Elliptic stable envelope for Hilbert scheme of points in the plane
• Instanton R-matrix and \(\mathcal{W}\)-symmetry
• \(t,q\)-deformed \(Q\)-systems, DAHA and quantum toroidal algebras via generalized Macdonald operators
• Finite type modules and Bethe ansatz for quantum toroidal \(\mathfrak{gl}_1\)
• Liouville reflection operator, affine Yangian and Bethe ansatz
• Moduli of flags of sheaves and their K-theory
• The Maulik–Okounkov R-matrix from the Ding–Iohara–Miki algebra
• A (q,γ) analog of the W1+∞ algebra
• A commutative algebra on degenerate CP1 and Macdonald polynomials
• Integrals of motion from quantum toroidal algebras
• Quantum toroidal $\mathfrak{g}{{\mathfrak{l}}_{1}}$ and Bethe ansatz
• Quantum groups and quantum cohomology

This page was built for publication: The \(R\)-matrix of the quantum toroidal algebra \(U_{q,t}(\overset{..}{gl}_1)\) in the Fock module