The Representation Theory of Hecke Algebras Through the Knizhnik-Zamolodchikov Functor

Work by V. Ginzburg, N. Guay, E. Opdam, R. Rouquier (2003) established a connection between the category of modules over Hecke algebras, and that of representations of rational Cherednik algebras through the Knizhnik-Zamolodchikov functor.

In this project, we aim to make use of this connection to provide a better understanding of the representation theory of Hecke algebras by studying the way the representations relate to the functor through the monodromy described in the aforementioned paper. In particular, the central goal is that we will explicitly compute representations of Hecke algebras parametrised by roots of unity associated to dihedral groups, and relate them back to results about rational Cherednik algebras through the Knizhnik-Zamolodchikov functor.

Muhammad Haris Rao

The University of Melbourne

Haris is finishing his second year of a bachelor of science degree at the University of Melbourne with the intention of majoring in pure mathematics.

Within mathematics, he is interested in a wide range of topics ranging from probability theory to mathematical logic, and recently, has been especially fascinated by the application of representation theoretic techniques in adjacent fields of algebra and geometry. Following the termination of his undergraduate studies at the end of 2022, he aims to continue with postgraduate studies in mathematics.

Outside of mathematics, Haris also enjoys going on walks or reading a nice book.

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