Correlation Functions of Quantum Toroidal gln Algebra

  •  Hao Cui    


In this paper, we study the correlation functions of the quantum toroidal \mathfrak{gl}_n algebra. Their first key properties are established in analogy to those of the correlation functions of quantum affine algebras U_q\mathfrak{n}_+. The core of the paper is the proof of the vanishing of those correlation functions at length 3 wheel conditions, which is done separately for n = 1, n = 2, n≥ 3 cases with different ``Master Equalities" of formal series (the n = 1 case has been previously discussed by the author in (Cui, 2021)). Another important contribution is the discovery of cubic Serre relations for the quantum toroidal.

This work is licensed under a Creative Commons Attribution 4.0 License.