Minuscule and cominuscule Hecke categories
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Type
ThesisThesis type
Doctor of PhilosophyAuthor/s
Baine, Joseph PatrickAbstract
This thesis considers various problems in classical and modular Kazhdan-Lusztig theory. The main results are:
- A complete determination of the antispherical p-Kazhdan-Lusztig bases of (co)minuscule Hecke categories in all characteristics;
- A complete determination of the spherical p-Kazhdan-Lusztig bases of (co)minuscule Hecke categories in good characteristic;
- A closed formula for the Jones-Wenzl idempotent in terms of the graded ranks of certain indecomposable Soergel bimodules; and
- A proof of the monotonicity of inverse Kazhdan-Lusztig polynomials.This thesis considers various problems in classical and modular Kazhdan-Lusztig theory. The main results are:
- A complete determination of the antispherical p-Kazhdan-Lusztig bases of (co)minuscule Hecke categories in all characteristics;
- A complete determination of the spherical p-Kazhdan-Lusztig bases of (co)minuscule Hecke categories in good characteristic;
- A closed formula for the Jones-Wenzl idempotent in terms of the graded ranks of certain indecomposable Soergel bimodules; and
- A proof of the monotonicity of inverse Kazhdan-Lusztig polynomials.
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Date
2024Rights statement
The author retains copyright of this thesis. It may only be used for the purposes of research and study. It must not be used for any other purposes and may not be transmitted or shared with others without prior permission.Faculty/School
Faculty of ScienceDepartment, Discipline or Centre
School of Mathematics and StatisticsAwarding institution
The University of SydneyShare