Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The Diagrammatic Spherical Category

Tasman Fell

Abstract

We construct a diagrammatic categorification of the spherical module over the Hecke algebra. We establish a basis for the morphism spaces of this category, and prove that it is equivalent to an existing algebraic spherical category.

The Diagrammatic Spherical Category

Abstract

We construct a diagrammatic categorification of the spherical module over the Hecke algebra. We establish a basis for the morphism spaces of this category, and prove that it is equivalent to an existing algebraic spherical category.
Paper Structure (29 sections, 46 theorems, 69 equations)

This paper contains 29 sections, 46 theorems, 69 equations.

Table of Contents

  1. Introduction
  2. Singular Soergel bimodules
  3. Structure of this paper
  4. Coxeter Systems and the Hecke Algebra
  5. The Hecke algebra and Kazhdan-Lusztig basis
  6. Trace and bilinear form on H
  7. The spherical and anti-spherical modules
  8. The Schur algebroid
  9. Realizations
  10. Graded rings and modules
  11. Singular Soergel Bimodules and Standard Bimodules
  12. Singular Soergel bimodules
  13. Standard bimodules and Localization
  14. Spherical Diagrammatics
  15. The diagrammatic category M_BS
  16. ...and 14 more sections

Key Result

Theorem 1.1

The collection $\mathcal{SDL}_{\underline{x}, \underline{y}}$ is a basis of Hom$_{\mathcal{M}_{BS}(J)}(\underline{x}, \underline{y})$ as a right $R$-module.

Theorems & Definitions (83)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Definition 2.1
  • Theorem 2.2: KL
  • Remark 2.3
  • Lemma 2.4: Bourbaki
  • Lemma 2.5: Deodhar1
  • Proposition 2.6
  • proof
  • ...and 73 more