Discovery Projects - Grant ID: DP150103431

Funding Activity

Website
http://dataportal.arc.gov.au/NCGP/Web/Grant/Grant/DP150103431

Funding Status
Closed

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Funded Activity Summary

The dimension problem for Hecke algebras. This project aims to give important new information about the graded Specht modules and the irreducible graded modules of the cyclotomic Hecke algebras. Experts have long considered that computing the dimensions of the irreducible representations to be completely intractable, however, the powerful new tools provided by the recently discovered KLR-grading gives rise to the combinatorics for solving this problem and for describing the graded decomposition numbers of these algebras. Even in characteristic zero this is incredibly interesting because, as a special case, it would give explicit combinatorial formulas for parabolic Kazhdan-Lusztig polynomials, a problem that has been studied intensely (without solution) for over thirty years.

Funded Activity Details

Start Date: 20-06-2015

End Date: 31-12-2019

Funding Scheme: Discovery Projects

Funding Amount: $399,500.00

Funder: Australian Research Council

Research Topics

ANZSRC Field of Research (FoR)

Combinatorics and Discrete Mathematics (excl. Physical Combinatorics) | Group Theory and Generalisations | Pure Mathematics | Algebra and Number Theory

ANZSRC Socio-Economic Objective (SEO)

Expanding Knowledge in the Mathematical Sciences |

Other Keywords

Algebra and Number Theory | Combinatorics and Discrete Mathematics (excl. Physical Combinatorics) | Expanding Knowledge in the Mathematical Sciences | Group Theory and Generalisations | Pure Mathematics

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