The representation theory of Hc(Sn~Z/lZ)

Hird, Niall (2022) The representation theory of Hc(Sn~Z/lZ). PhD thesis, University of Glasgow.

Abstract

In this thesis we examine various aspects of the representation theory of the restricted rational Cherednik algebra Hc(Sn~Z/lZ). We prove several multiplicity results for graded modules, in particular for modules over an algebra that admits a triangular decomposition. This includes the algebra Hc(Sn~Z/lZ). Furthermore, if the projective covers admit a radical preserving filtration, we show that we can calculate the multiplicities of the simple modules inside the radical layers of the projective covers.

We give an explicit presentation of the centre of the restricted rational Cherednik algebra Hc(Sn~Z/lZ) for suitably generic c. This is done by first deriving a presentation of the centre of Hc(Sn) using Schubert cells, then extending this to the more general wreath product group using the action of the cyclic group Z/lZ. This presentation is given for each block of the centre. Using the bijection between irreducible representations of Sn~Z/lZ and l-multipartitions of n, we prove that this explicit presentation can be read directly from the l-multipartition of n.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics
• Supervisor's Name: Bellamy, Professor Gwyn
• Date of Award: 2022
• Depositing User: Theses Team
• Unique ID: glathesis:2022-82740
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 09 Mar 2022 11:39
• Last Modified: 08 Apr 2022 16:45
• Thesis DOI: 10.5525/gla.thesis.82740
• URI: https://theses.gla.ac.uk/id/eprint/82740