The derived category of representations of the special linear group of degree two over a finite field

Wong, W. H. Y. (2016). The derived category of representations of the special linear group of degree two over a finite field. (Unpublished Doctoral thesis, City, University of London)

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Abstract

In this thesis, we study the modular representations of the special linear group of degree two over a finite field in defining characteristic. In particular, we study the automorphisms of derived category of representations. We have been able to obtain a new type of autoequivalence.

This autoequivalence has some uncommon features. It is more conveniently conceived and proved using the representation theory of its Brauer subgroup but at the same time it can be very neatly described, using a type of derived equivalence called perverse equivalence, in global settings.

Item Type: Thesis (Doctoral)
Subjects: Q Science > QA Mathematics
Divisions: School of Engineering & Mathematical Sciences
URI: http://openaccess.city.ac.uk/id/eprint/15824

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