Cylindric symmetric functions and quantum integrable systems

QA Mathematics

Palazzo, David ; Korff, Christian

University:University of Glasgow

Department:School of Mathematics and Statistics

关键词: Symmetric functions, cylindric symmetric functions, integrable systems, Yang-Baxter equation, Frobenius Algebras.;   

Others  :  http://theses.gla.ac.uk/41216/7/2019palazzophd.pdf

来源: University of Glasgow

【 摘 要 】

We employ the level-n action of the affine symmetric group to construct cylindric versions of elementary and complete symmetric functions. We identify their expansions in terms of the bases of ordinary elementary and complete symmetric functions with the structure constants of generalised Verlinde algebras. Then we describe statistical vertex models associated to the q-boson model, when evaluated at q=1, and study the interplay between the partition functions of these models and the cylindric symmetric functions introduced above.