Computing the R-matrix of the quantum toroidal algebra
Name
011702_1_online.pdf
Description
Published version
Size
4.29 MB
Format
Adobe PDF
Checksum (MD5)
05d863abb45ab44537a43865497cb6e4
Author(s)
Garbali, Alexandr
Neguţ, Andrei
Date Issued
January 24, 2023
Journal
Journal of Mathematical Physics
Publisher
AIP Publishing
Citation
Alexandr Garbali, Andrei Neguţ; Computing the R-matrix of the quantum toroidal algebra. J. Math. Phys. 1 January 2023; 64 (1): 011702.
Version
Final published version
Abstract
We consider the problem of the R-matrix of the quantum toroidal algebra Uq,t(gl..1) in the Fock representation. Using the connection between the R-matrix R(u) (u being the spectral parameter) and the theory of Macdonald operators, we obtain explicit formulas for R(u) in the operator and matrix forms. These formulas are expressed in terms of the eigenvalues of a certain Macdonald operator, which completely describe the functional dependence of R(u) on the spectral parameter u. We then consider the geometric R-matrix (obtained from the theory of K-theoretic stable bases on moduli spaces of framed sheaves), which is expected to coincide with R(u) and thus gives another approach to the study of the poles of the R-matrix as a function of u.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1063/5.0120003
