Alphabeta MathCyclotomic Hecke and Quiver Hecke Algebras — Examples
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1 · Prerequisites
Abstract Algebra
- Algebraic Closure, Embeddings, and Separability
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Braid Groups
Categorification and Geometric Representation Theory
- Cyclotomic Hecke and Quiver Hecke Algebras
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- Divided Powers, Integral Forms, and Quantum Highest Weights
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2 · Logical flowchart
3 · Items
Example
Homogeneous degree check for the corrected KLR braid relation
Example
The degenerate level-one Hecke–KLR map for S₃
Example
The level-one rank-two cyclotomic KLR algebra at e=3
Counterexample
At positive rank the whole affine Hecke algebra is not one cyclotomic KLR block
Sources
- Mikhail Khovanov and Aaron D. Lauda, A diagrammatic approach to categorification of quantum groups I, arXiv:0803.4121v3, Represent. Theory 13 (2009) 309–347 (complete 53-page article)
- Jonathan Brundan and Alexander Kleshchev, Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras, arXiv:0808.2032v3, Invent. Math. 178 (2009) 451–484 (complete 32-page article)
- Alexander Kleshchev, Representation theory of symmetric groups and related Hecke algebras, arXiv:0909.4844v1, Bull. AMS 47 (2010) 419–481 (complete 66-page survey)
- Jonathan Brundan and Alexander Kleshchev, Blocks of cyclotomic Hecke algebras and Khovanov–Lauda algebras, arXiv:0808.2032v3, Invent. Math. 178 (2009) 451–484 (complete 32-page article)
- Jun Hu and Andrew Mathas, Seminormal forms and cyclotomic quiver Hecke algebras of type A, arXiv:1304.0906v3 (published in Math. Ann.), complete 51-page article
- Jonathan Brundan and Alexander Kleshchev, Graded decomposition numbers for cyclotomic Hecke algebras, arXiv:0901.4450v3, Adv. Math. 222 (2009) 1883–1942 (complete 57-page article)