8 papers · 1 filter
Langlands correspondence and Bezrukavnikov's equivalence
Anna Romanov, Geordie Williamson
These are lecture notes (by the first author) from a course (by the second author) given over two extended semesters at the University of Sydney. The first part provides an introdu…
Lectures on the Geometry and Modular Representation Theory of Algebraic Groups
Joshua Ciappara, Geordie Williamson
These notes provide a concise introduction to the representation theory of reductive algebraic groups in positive characteristic, with an emphasis on Lusztig's character formula an…
Modular representations and reflection subgroups
Geordie Williamson
The Hecke category is at the heart of several fundamental questions in modular representation theory. We emphasise the role of the "philosophy of deformations" both as a conceptual…
A simple character formula
Simon Riche, Geordie Williamson
In this paper we prove a character formula expressing the classes of simple representations in the principal block of a simply-connected semisimple algebraic group G in terms of ba…
Parity sheaves and the Hecke category
Geordie Williamson
The Hecke category is emerging as a fundamental object in representation theory. We give a motivated introduction to this category in both its geometric (via parity sheaves) and di…
A non-perverse Soergel bimodule in type A
Nicolas Libedinsky, Geordie Williamson
A basic question concerning indecomposable Soergel bimodules is to understand their endomorphism rings. In characteristic zero all degree-zero endomorphisms are isomorphisms (a fac…