Subalgebras of the Cherednik algebra occurring within Howe duality

Kieran Calvert (University of Manchester)

Wednesday 14th September, 2022 16:00-17:00 Maths 311B

Abstract

Howe duality describes the pairing of two groups within differentiation and multiplication of polynomials (the Weyl algebra). Deforming this differentiation to Dunkl operators defines the Cherednik algebra. I will explain some cases of deformed Howe duality within the Cherednik algebra; recent results on the subalgebras occurring within this duality and future directions. This includes a description of the centre of the Dunkl total angular momentum algebra, Dirac operators for the centre of the Dunkl angular momentum algebra and future work towards higher deformed Howe duality.

This is joint work With Marcelo De Martino and Roy Oste.

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