Ding-Iohara-Miki symmetry of network matrix models

Abstract

Ward identities in the most general "network matrix model" can be described in terms of the Ding-Iohara-Miki algebras (DIM). This confirms an expectation that such algebras and their various limits/reductions are the relevant substitutes/deformations of the Virasoro/W-algebra for (q, t) and (q_1, q_2, q_3) deformed network matrix models. Exhaustive for these purposes should be the Pagoda triple-affine elliptic DIM, which corresponds to networks associated with 6d gauge theories with adjoint matter (double elliptic systems). We provide some details on elliptic qq-characters.

20 pages, 2 figures

References in corpus (25)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• On AGT relation in the case of U(3)
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• Instantons and Merons in Matrix Models
• Matrix model version of AGT conjecture and generalized Selberg integrals
• Superconformal Partition Functions and Non-perturbative Topological Strings
• Seiberg-Witten theory and matrix models
• AGT conjecture and Integrable structure of Conformal field theory for c=1
• Notes on Ding-Iohara algebra and AGT conjecture
• Partition Functions of Matrix Models as the First Special Functions of String Theory. II. Kontsevich Model
• Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
• On "Dotsenko-Fateev" representation of the toric conformal blocks
• Kernel function and quantum algebras
• Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics
• ADE Little String Theory on a Riemann Surface (and Triality)
• $q$-Virasoro/W Algebra at Root of Unity and Parafermions
• Wall Crossing Invariants: from quantum mechanics to knots
• Quantum toroidal gl(1) and Bethe ansatz
• W(1+infinity) algebra as a symmetry behind AGT relation
• Virasoro constraint for Nekrasov instanton partition function
• Seiberg-Witten curves and double-elliptic integrable systems
• Representations of quantum toroidal $g{l}_n$
• Polynomials associated with fixed points on the instanton moduli space
• A presentation of the deformed W_{1+\infty} algebra

Cited by in corpus (80)

• Explicit examples of DIM constraints for network matrix models
• Webs of W-algebras
• (p,q)-webs of DIM representations, 5d N=1 instanton partition functions and qq-characters
• $(q,t)$-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces
• Flipping the head of T[SU(N)]: mirror symmetry, spectral duality and monopoles
• On (q,t)-deformation of Gaussian matrix model
• Quiver Yangian and Supersymmetric Quantum Mechanics
• Anomaly in RTT relation for DIM algebra and network matrix models
• Sum rules for characters from character-preservation property of matrix models
• Reflection states in Ding-Iohara-Miki algebra and brane-web for D-type quiver
• Quiver elliptic W-algebras
• A slow review of the AGT correspondence
• Shifted Quiver Quantum Toroidal Algebra and Subcrystal Representations
• $\mathcal{W}$-algebra Modules, Free Fields, and Gukov-Witten Defects
• (q,t)-KZ equation for Ding-Iohara-Miki algebra
• Higgsed network calculus
• On determinant representation and integrability of Nekrasov functions
• $q$-Virasoro modular double and 3d partition functions
• Nambu bracket and M-theory
• Refined geometric transition and $qq$-characters
• A note on the algebraic engineering of 4D $\mathcal{N}=2$ super Yang-Mills theories
• On $W$-representations of $\beta$- and $q,t$-deformed matrix models
• The MacMahon R-matrix
• New quantum toroidal algebras from 5D $\mathcal{N}=1$ instantons on orbifolds
• 3d Mirror Symmetry from S-duality
• $(q,t)$-deformed (skew) Hurwitz $\tau$-functions
• An analogue of Schur functions for the plane partitions
• Maulik-Okounkov's R-matrix from Ding-Iohara-Miki algebra
• Hunt for 3-Schur polynomials
• Solving q-Virasoro constraints
• Fiber-base duality from the algebraic perspective
• Mixed network calculus
• On the Quantization of Seiberg-Witten Geometry
• Commutative families in $W_{\infty }$, integrable many-body systems and hypergeometric $\tau$-functions
• Cauchy formula and the character ring
• On Factorization of Generalized Macdonald Polynomials
• Symmetry enhancements via 5d instantons, qW-algebrae and (1,0) superconformal index
• On complete solution of the quantum Dell system
• 5d AGT correspondence of supergroup gauge theories from quantum toroidal ${\mathfrak{gl}}_1$
• Orthogonal Polynomials in Mathematical Physics
• Kerov functions for composite representations and Macdonald ideal
• q-Painleve equation from Virasoro constraints
• A non-torus link from topological vertex
• Elliptic modular double and 4d partition functions
• Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function
• Can tangle calculus be applicable to hyperpolynomials?
• On $6j$-symbols for symmetric representations of $U_q({\mathfrak{su}}_N)$
• Bootstrapping the $S^5$ partition function
• Self-dual form of Ruijsenaars-Schneider models and ILW equation with discrete Laplacian
• Exact SUSY Wilson loops on $S^3$ from $q$-Virasoro constraints
• Simple Representations of BPS Algebras: the case of $Y({\widehat{\mathfrak{gl}}}_2)$
• 3-Schurs from explicit representation of Yangian $Y({\widehat{\mathfrak{gl}}}_1)$. Levels 1-5
• Check-Operators and Quantum Spectral Curves
• Correlators in the supereigenvalue model in the Ramond sector
• On the status of DELL systems
• Argyres-Douglas Theories, S-duality and AGT Correspondence
• Refined toric branes, surface operators and factorization of generalized Macdonald polynomials
• On generalized Macdonald polynomials
• Shifted quantum groups and matter multiplets in supersymmetric gauge theories
• Why Is Landau-Ginzburg Link Cohomology Equivalent To Khovanov Homology?
• Modular properties of 6d (DELL) systems
• Exact correlators in the Gaussian Hermitian matrix model
• Irreducible representations of simple Lie algebras by differential operators
• $W_{1+\infty }$ constraints for the hermitian one-matrix model
• Quantum Geometry and $\theta$-Angle in Five-Dimensional Super Yang-Mills
• Quantum integrability of $\mathcal{N}=2$ 4d gauge theories
• Engineering 3D $\mathcal{N}=2$ theories using the quantum affine $\mathfrak{sl}(2)$ algebra
• Supersymmetric Wilson Loops, Instantons, and Deformed $\mathcal{W}$-Algebras
• Towards the theory of Yangians
• Seiberg-Witten period relations in Omega background
• Hopf superpolynomial from topological vertices
• Elliptic algebra, Frenkel-Kac construction and root of unity limit
• Non-Perturbative Schwinger-Dyson Equations for 3d $\mathcal{N}=4$ Gauge Theories
• The Grassmannian VOA
• Interrelations between dualities in classical integrable systems and classical-classical version of quantum-classical duality
• Diamond of triads
• Free field realization of the Ding-Iohara algebra at general levels
• Intertwining operator and integrable hierarchies from topological strings
• From superintegrability to tridiagonal representation of $\beta$-ensembles
• Quantum differential and difference equations for ${\mathrm{Hilb}}^n({\mathbb{C}}^2)$