Elliptic Ding-Iohara Algebra and the Free Field Realization of the Elliptic Macdonald Operator

Abstract

The Ding-Iohara algebra is a quantum algebra arising from the free field realization of the Macdonald operator. Starting from the elliptic kernel function introduced by Komori, Noumi and Shiraishi, we can define an elliptic analog of the Ding-Iohara algebra. The free field realization of the elliptic Macdonald operator is also constructed.

42 pages

References in corpus (4)

• Essays on the theory of elliptic hypergeometric functions
• Quantum Algebraic Approach to Refined Topological Vertex
• Notes on Ding-Iohara algebra and AGT conjecture
• Kernel Functions for Difference Operators of Ruijsenaars Type and Their Applications

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• An M-Theoretic Derivation of a 5d and 6d AGT Correspondence, and Relativistic and Elliptized Integrable Systems
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• A Macdonald refined topological vertex
• Higher AGT Correspondences, W-algebras, and Higher Quantum Geometric Langlands Duality from M-Theory
• Commutative Families of the Elliptic Macdonald Operator
• Elliptic Ding-Iohara Algebra and Commutative Families of the Elliptic Macdonald Operator
• MacMahon KZ equation for Ding-Iohara-Miki algebra
• Free field approach to the Macdonald process