5 papers
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…
Koszul duality for Kac-Moody groups and characters of tilting modules
Pramod Achar, Shotaro Makisumi, Simon Riche +1
We establish a character formula for indecomposable tilting modules for connected reductive groups in characteristic p in terms of p-Kazhdan-Lusztig polynomials, for p>h the Coxete…
The Hodge theory of the Decomposition Theorem (after de Cataldo and Migliorini)
Geordie Williamson
In its simplest form the Decomposition Theorem asserts that the rational intersection cohomology of a complex projective variety occurs as a summand of the cohomology of any resolu…
On the character of certain tilting modules
George Lusztig, Geordie Williamson
Let G be a semisimple group over an algebraically closed field of characteristic p>0. We give a (partly conjectural) simple, closed formula for the character of many indecomposable…