Cylindric symmetric functions and quantum integrable systems

Palazzo, David (2019) Cylindric symmetric functions and quantum integrable systems. PhD thesis, University of Glasgow.

Abstract

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.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Keywords: Symmetric functions, cylindric symmetric functions, integrable systems, Yang-Baxter equation, Frobenius Algebras.
• Subjects: Q Science > QA Mathematics
• Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Supervisor's Name: Korff, Dr. Christian
• Date of Award: 2019
• Depositing User: Mr David Palazzo
• Unique ID: glathesis:2019-41216
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 06 May 2019 08:27
• Last Modified: 05 Mar 2020 21:35
• Thesis DOI: 10.5525/gla.thesis.41216
• URI: https://theses.gla.ac.uk/id/eprint/41216