Matrix Product Multi-Variable Polynomials From Quantum Algebras

Abstract

This project aims to expand the theory of polynomials and develop generalised polynomial families using connections to affine and toroidal algebras. Many combinatorial and computational problems in pure and applied mathematics as well as mathematical physics can be solved using polynomials in many variables, such as Macdonald polynomials. This project is anticipated to address the current difficulty of implementing symmetric and non-symmetric polynomials in symbolic algebra packages by developing completely new algorithms. New understanding from the project is expected to facilitate challenging computational problems of measurable quantities in quantum systems.