Solutions to the reflection equation: A bijection between lattice configurations and marked shifted tableaux

Clark, Mary (2014) Solutions to the reflection equation: A bijection between lattice configurations and marked shifted tableaux. MSc(R) thesis, University of Glasgow.

Abstract

This thesis relates Young tableaux and marked shifted tableaux with non-intersecting lattice paths. These lattice paths are generated by certain exactly solvable statistical mechanics models, including the vicious and osculating walkers. These models arise from solutions to the Yang-Baxter and Reflection equations. The Yang-Baxter Equation is a consistency condition in integrable systems; the Reflection Equation is a generalisation of the Yang-Baxter equation to systems which have a boundary. We further establish a bijection between two types of marked shifted tableaux.

• Item Type: Thesis (MSc(R))
• Qualification Level: Masters
• 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: 2014
• Depositing User: Miss Mary Clark
• Unique ID: glathesis:2014-5865
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 18 Dec 2014 09:21
• Last Modified: 18 Dec 2014 09:57
• URI: https://theses.gla.ac.uk/id/eprint/5865