University of Birmingham > Talks@bham > Birmingham and Warwick Algebra Seminar  > Twists in representation theory

Twists in representation theory

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If you have a question about this talk, please contact Chris Parker.

Very roughly, quantisation in algebra is about taking a commutative structure and using ideas and constructions inspired by physics make it noncommutative; then finding out what does not work and what does (and what works even better than in the commutative case). I will talk about one type of quantisation known as cocycle twisting, when the product on an associative algebra A is replaced by a new, “deformed” product. I am interested in how the representation theory of this deformed version of A differs from that of A. Cocycles which can be used for twisting arise from equations which are very difficult to solve, but in my talk I will focus on a simple case when the cocycle arises from an action on A by a finite non-cyclic abelian group – something referred to as discrete torsion by Vafa and Witten. I will show how such discrete torsion can deform a Coxeter group, leading to “mystic reflection groups” which have well-behaved invariants when they act on polynomials in skew-commuting variables. If time permits, I will mention recent work of Berenstein, Jones-Healey, McGaw and myself on representations on twisted Cherednik algebras.

This talk is part of the Birmingham and Warwick Algebra Seminar series.

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