KZ-Functor for Rational Cherednik Algebras

Knizhnik–Zamolodchikov (KZ) functor is a useful tool in Representation Theory. We intend to develop a better understanding of the KZ-functor via explicit examples. We explore certain representations of the rational Cherednik algebras attached to cyclic groups, and investigate how the KZ functor maps such modules to representations of the corresponding Hecke algebras with parameters at roots of unity. We then extend our investigation to other complex reflection groups, such as the symmetric groups.

Yifan Guo

The University of Melbourne

Yifan is a third-year Bachelor of Science student from the University of Melbourne, studying a major in pure mathematics with a concurrent diploma in computing. She loves mathematics for its power to connect seemingly disparate concepts and enjoys learning about a range of mathematical fields. Yifan is particularly drawn to algebra and has been an active member of the representation theory student seminar group at her university. She also recently gave an introductory talk related to the Macdonald polynomials. Yifan was awarded the Dixson Prize in Pure Mathematics in 2020 and is also a recipient of the Melbourne Chancellor’s Scholarship. Aside from her studies, Yifan is a former President of Melbourne University Mathematics and Statistics Society from 2020–2021. She also enjoys helping high-school students from disadvantaged backgrounds through mentoring at the Institute for Enquiring Minds.

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