Modular Representation Theory
Notes on Calder Morton-Ferguson's lectures at Stanford, 2025 Spring.
Introduction
Calder's course
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Introduction
Classification of Simple Modules
Calder's class
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Classification of Simple Modules
Lusztig' Character Formula
Calder's class
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Lusztig' Character Formula
Soegel's Modular Category $\mathcal{O}$
Calder's class
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Soegel's Modular Category $\mathcal{O}$
Soegel Bimodules
Calder's class
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Soegel Bimodules
Parity-sheaves
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Parity-sheaves
Tilting modules
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Tilting modules
Williamson's Counterexample
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Williamson's Counterexample
Highest Weight Categories
Lecture 9 of Calder's course
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Highest Weight Categories
Tilting character formula
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Tilting character formula
Proof of Finkelberg-Mirkovic Conjecture
Calder's course
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Proof of Finkelberg-Mirkovic Conjecture
Representation of $G(\mathbb{F}_ {q})$
Calder's course
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Representation of $G(\mathbb{F}_ {q})$
Lusztig's Conjecture
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Lusztig's Conjecture
Nice Basis
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Nice Basis
Consruction of $M_ {w}$
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Consruction of $M_ {w}$
Uniquenss of $M_ {w}$ and Failure of Lusztig's Conjecture
Calder's course
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Uniquenss of $M_ {w}$ and Failure of Lusztig's Conjecture
Exceptional Collection
Calder's course
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Exceptional Collection