Soergel Calculus

By Benita Elias, Geordie Williamson. 2013

187 citations recorded by the source corpus.

The monoidal category of Soergel bimodules is an incarnation of the Hecke category, a fundamental object in representation theory. We present this category by generators and relations, using the language of planar diagrammatics. We show that Libedinsky’s light leaves give a basis for morphism spaces and give a new proof of Soergel’s classification of the indecomposable Soergel bimodules.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/1566a5c3ea74d884b0632daacc76a3196229c0b9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Ben Elias
2. Geordie Williamson
3. L. T. Jensen

In Discrete Mathematics and Combinatorics

1. Geordie Williamson
2. Ben Elias
3. L. T. Jensen
4. Simon Riche
5. Jonathan Brundan
6. C. Stroppel

In Geometry and Topology

1. Ben Elias
2. Geordie Williamson
3. L. T. Jensen
4. C. Stroppel
5. Simon Riche
6. Jonathan Brundan

Citations in the corpus

• The Hodge theory of Soergel bimodules (2012, methodology): “We discuss the choice of representation in detail in [EWb], where we give alternative proofs of the results of [Soe07] which are valid when h is any “realization” of W .”
• The two-color Soergel calculus (2013, background): “rticular, we only need to assume Demazure surjectivity. However, the proof of the SCT in this paper also relies on local non-degeneracy and lesser invertibility as well. For a more general proof, see [11]. 6.2.1. Definitions. Definition 6.15. A Soergel graph for m<∞ is an isotopy class of a particu”