Elliptic Ding-Iohara Algebra and Commutative Families of the Elliptic Macdonald Operator

Abstract

The elliptic Ding-Iohara algebra is an elliptic quantum group obtained from the free field realization of the elliptic Macdonald operator. In this article, we show the construction of two families of commuting operators which contain the elliptic Macdonald operator by using the elliptic Ding-Iohara algebra and the elliptic Feigin-Odesskii algebra.

21 pages. This article is based on the talk given by the author at "16 th Workshop on Representation Theory of Algebraic Groups and Quantum Groups" (June, 2013). arXiv admin note: text overlap with arXiv:1305.7097

References in corpus (5)

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

Cited by in corpus (5)

• Explicit examples of DIM constraints for network matrix models
• (q,t)-KZ equation for Ding-Iohara-Miki algebra
• Macdonald topological vertices and brane condensates
• An elliptic topological vertex
• A Macdonald refined topological vertex