Abstract
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.
Highlights
The quantum toroidal gln algebras, where n > 2, were introduced more than 20 years ago in (Ginzburg, 1995)
We study the correlation functions of the quantum toroidal gl1 algebra
The proper definition of the quantum toroidal algebra of gl2 was given only recently in (Feigin, 2011). Another combinatorial perspective to the quantum toroidal algebras is given via the trigonometric version of the FeiginOdesskii shuffle algebras of (Feigin, 1997), (Negut, 2013), (Negut, 2014) and (Tsymbaiuk, 2018)
Summary
The quantum toroidal gln algebras, where n > 2, were introduced more than 20 years ago in (Ginzburg, 1995). The proper definition of the quantum toroidal algebra of gl was given only recently in (Feigin, 2011). The main objective of this paper is to establish similar properties of the correlation functions of the quantum toroidal algebras, providing an interesting perspective to the “wheel” conditions in that setup. The case of quantum toroidal algebras is interesting in the setup of gln, since this is the only case when one has two deformation parameters instead of one.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
