Polynomial Representations of the Hecke Algebra (ARC Discovery Project administered by the University of Melbourne) (2009-2011)

Multivariate polynomials are of great importance and interest in many areas of mathematics. This proposal aims to further develop the theory of such polynomials using the representation theory of Hecke algebras and techniques from exactly solvable lattice models. A further aim is to develop a toolkit for working with multivariate polynomials within standard software systems such as Maple and Mathematica. Currently, such software implementations for these systems are highly inadequate. One of the expected outcomes is an online database with software libraries for computing with multivariate polynomials.