Alphabeta MathUnequal-Parameter Hecke Cells and Representations: Examples and Counterexamples
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1 · Prerequisites
Abstract Algebra
- Algebraic Extensions, Extension Degree, and Finite Fields
- Binary Operations, Monoids, Groups and Subgroups
- Chain Conditions, Semisimple Modules and the Wedderburn–Artin Theorem
- Cosets, Index and Lagrange's Theorem
- Cyclic Groups and Direct Products
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- Group Homomorphisms and the Isomorphism Theorems
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- Normal Subgroups and Quotient Groups
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- Rings, Subrings, Integral Domains and Fields
- Simple Field Extensions and the Construction of the Complex Numbers
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- The Field of Fractions and Localisation
- The Fundamental Theorem of Finite Abelian Groups
Categorification and Geometric Representation Theory
Category Theory
Combinatorics
Commutative Algebra
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Coxeter Groups
Group Theory
Linear Algebra
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Number Theory
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Set Theory
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2 · Logical flowchart
3 · Items
Example
A B2 unequal-parameter KL basis and four left-cell transitions
Counterexample
A characteristic-two specialization collapses four weighted cell labels
Example
A nonsemisimple L-good rank-one specialization has a singleton basic set
Sources
- George Lusztig, Hecke Algebras with Unequal Parameters, revised arXiv text (2014)
- Anders Björner and Francesco Brenti, Combinatorics of Coxeter Groups, GTM 231 (2005)
- Meinolf Geck, Modular Representations of Hecke Algebras, EPFL lecture notes (2006)
- Meinolf Geck, Modular Representations of Hecke Algebras, sections 4–6
- George Lusztig, Hecke Algebras with Unequal Parameters, revised text, sections 18–21