Alphabeta MathOrdinary Hecke Specht Polytabloids and Signed Murphy Comparison — Examples
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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
- Divisibility, Euclidean Domains, Principal Ideal Domains and Unique Factorisation
- Free Groups and Presentations
- Free Modules, Exact Sequences, Projective and Injective Modules
- Group Actions, Orbits, Stabilisers and Cayley's Theorem
- Group Homomorphisms and the Isomorphism Theorems
- Ideals, Quotient Rings and the Isomorphism Theorems for Rings
- Modules, Submodules, Quotient Modules and the Isomorphism Theorems
- Normal Subgroups and Quotient Groups
- Polynomial Rings, the Division Algorithm and Roots
- Rings, Subrings, Integral Domains and Fields
- Simple Field Extensions and the Construction of the Complex Numbers
- Splitting Fields
- Tensor Products of Modules
- The Group Algebra and Representations of Finite Groups
Categorification and Geometric Representation Theory
Category Theory
Commutative Algebra
Coxeter Groups
Group Theory
Linear Algebra
- Determinants of Matrices over a Commutative Ring
- Gaussian Elimination, Elementary Matrices and Reduced Row Echelon Form
- Linear Independence, Bases and Dimension
- Linear Transformations, Rank-Nullity and Quotient Spaces
- Matrices, the Matrix of a Linear Map, and Change of Basis
- Vector Spaces, Linear Subspaces, Span and Direct Sums
Number Theory
Real Analysis
Representation Theory of Groups
Set Theory
2 · Logical flowchart
3 · Items
Counterexample
Untwisted conjugation changes the module
Example
The row and column Specht conventions in rank three
Example
The two-tableau pairing at a singular parameter
Sources
- G. D. James, The Representation Theory of the Symmetric Groups, Lecture Notes in Mathematics 682, Springer 1978; author-hosted scan
- Andrew Mathas, Iwahori-Hecke algebras and Schur algebras of the symmetric group, author-hosted prepublication manuscript, 79 PDF pages
- Steen Ryom-Hansen, On the denominators of Young's seminormal basis, arXiv:0904.4243v5, 28 PDF pages