Representation Theory: Path Models and Decompositions

Grant number: DP0986774 | Funding period: 2009 - 2012

Completed

Abstract

The research in this proposal develops tools for capitalising on the benefits of symmetry in large complex systems. These techniques and processes are applicable for solving complex problems in large interactive systems. This project will involve young researchers and train them for problem solving in a wealth of fields, including management, the sciences, the financial industries, and the development of technologies. The research is in one of the most active cutting edge areas of pure mathematics and will contribute to maintaining Australia's position as a leading nationality in research in representation theory and its applications.

Related publications (7)

Hopf algebras and Markov chains: Two examples and a theory

P Diaconis, CYA Pang, A Ram

2014-01-01

The operation of squaring (coproduct followed by product) in a combinatorial Hopf algebra is shown to induce a Markov chain in nat..

Generalized Schubert Calculus

Nora Ganter, Arun Ram

2013-07-01

Affine and degenerate affine BMW algebras: Actions on tensor space

Z Daugherty, A Ram, R Virk

2013-05-01

The affine and degenerate affine Birman-Murakami-Wenzl (BMW) algebras arise naturally in the context of Schur-Weyl duality for ort..

A probabilistic interpretation of the MacDonald polynomials

P Diaconis, A Ram

2012-12-01

The two-parameter Macdonald polynomials are a central object of algebraic combinatorics and representation theory. We give a Marko..

Universal graded Specht modules for cyclotomic Hecke algebras

AS Kleshchev, A Mathas, A Ram

2012-12-01

The graded Specht module S for a cyclotomic Hecke algebra comes with a distinguished generating vector z∈S, which can be thought o..

Representations of Khovanov-Lauda-Rouquier algebras and combinatorics of Lyndon words

A Kleshchev, A Ram

2011-04-01

We construct irreducible representations of affine Khovanov-Lauda-Rouquier algebras of arbitrary finite type. The irreducible repr..

Universal Verma modules and the Misra-Miwa Fock space

P Tingley, A Ram

2010-12-01

The Misra-Miwa v -deformed Fock space is a representation of the quantized affine algebra U v (s l ). It has a standard basis inde..

University of Melbourne Researchers

Arun Ram