110 research outputs found
Combinatorial Representation Theory
We attempt to survey the field of combinatorial representation theory,
describe the main results and main questions and give an update of its current
status. We give a personal viewpoint on the field, while remaining aware that
there is much important and beautiful work that we have not been able to
mention
Recommended from our members
Computational Group Theory
This was the seventh workshop on Computational Group Theory. It showed that Computational Group Theory has significantly expanded its range of activities. For example, symbolic computations with groups and their representations and computations with infinite groups play a major role nowadays. The talks also presented connections and applications to cryptography, number theory and the algorithmic theory of algebras
Parity sheaves and the Hecke category
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 diagrammatic (generators and relations) incarnations.
We also discuss the p-canonical basis and Koszul duality for the Hecke
category.Comment: ICM repor
On Iwahori-Whittaker Functions for Metaplectic Groups
We relate Iwahori-Whittaker functions on metaplectic covers to certain
Demazure-Lusztig operators, the latter of which are built from a Weyl group
action previously considered by G. Chinta and P. Gunnells. Using a certain
combinatorial identity for the sum of these Demazure-Lusztig operators, we
obtain an analogue of the Casselman-Shalika formula for spherical Whittaker
functions in this context.Comment: Previous version had title "On the Casselman-Shalika formula for
metaplectic groups
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