Yang-Baxter algebras as convolution algebras: the Grassmannian case

Gorbounov, V., Korff, C. and Stroppel, C. (2020) Yang-Baxter algebras as convolution algebras: the Grassmannian case. Russian Mathematical Surveys, (Accepted for Publication)

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Abstract

We present a simple but explicit example of a recent development which connects quantum integrable models with Schubert calculus: there is a purely geometric construction of solutions to the Yang-Baxter equation and their associated Yang-Baxter algebras which play a central role in quantum integrable systems and exactly solvable lattice models in statistical physics. We consider the degenerate five-vertex limit of the asymmetric six-vertex model and identify its associated Yang-Baxter algebra as convolution algebra arising from the equivariant Schubert calculus of Grassmannians. We show how our method can be used to construct (Schur algebra type) quotients of the current algebra gl2[t] acting on the tensor product of copies of its evaluation representation C2[t]. Finally we connect it with the COHA for the A1-quiver.

Item Type:Articles
Status:Accepted for Publication
Refereed:Yes
Glasgow Author(s) Enlighten ID:Korff, Dr Christian
Authors: Gorbounov, V., Korff, C., and Stroppel, C.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Research Group:Mathematical Physics and Integrable Systems
Journal Name:Russian Mathematical Surveys
Publisher:Turpion
ISSN:0036-0279
ISSN (Online):1468-4829
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