Open AccessCorrelation Functions of Quantum Toroidal $\mathfrak{gl}_1$ Algebra
Author(s) -
Hao Chen
Publication year - 2021
Publication title -
journal of mathematics research
Language(s) - English
Resource type - Journals
eISSN - 1916-9809
pISSN - 1916-9795
DOI - 10.5539/jmr.v13n2p7
Subject(s) - mathematics , quantum , algebra over a field , quantum affine algebra , toroid , series (stratigraphy) , key (lock) , correlation , affine transformation , pure mathematics , quantum mechanics , geometry , algebra representation , cellular algebra , physics , paleontology , ecology , plasma , biology
In this paper, we study the correlation functions of the quantum toroidal $\mathfrak{gl}_1$ algebra. The first key properties we establish are similar to those of the correlation functions of quantum affine algebras $U_q\mathfrak{n}_+$ as established by Enriquez in (Eneiquez, 2000), while the proof of the remaining key ``vanishing property" relies on a certain ``Master Equality'' of formal series, which constitutes the main technical result of this paper.