Primary literature and authoritative references

Follow the evidence.

Source pages connect bibliography entries to the claims that depend on them. Locators are attached to individual mathematical assertions.

Source	Type	Dependent assertions
Zuber · Invariances in Physics and Group Theory	lecture-notes	1
Haber · Spin covers and subgroup examples	lecture-notes	43
Bekaert and Boulanger · Poincaré representations	paper	0
GAP · Character tables and Frobenius–Schur indicators	documentation	274
Conrad and Landesman · Compact Lie groups	lecture-notes	794
SageMath · Weyl characters	documentation	416
SageMath · Branching rules	documentation	0
GAP · Characters and symmetrizations	documentation	342
GroupNames · A₄	database	48
Aharony, Seiberg and Tachikawa · Global gauge structure	paper	2
Tong · Line operators in the Standard Model	paper	112
McKay · A rapid introduction to ADE theory	paper	1
Kibble · Topology of cosmic domains and strings	paper	0
LMFDB · Abstract groups	database	0
Ishimori et al. · Discrete symmetries in particle physics	paper	2
Henning et al. · Hilbert series and operator bases	paper	0
GroupNames: C₃	database	41
GroupNames: S₃	database	39
GroupNames: S₄	database	56
GroupNames: A₅	database	57
GroupNames: Q₈	database	55
GroupNames: D₈	database	56
Finite simple groups: Lecture 1 — Introduction and alternating groups	lecture-notes	43
Finite simple groups: Lecture 2 — Linear groups	lecture-notes	5
Finite simple groups: Lecture 3 — Classical groups	lecture-notes	11
Classical groups: detailed lecture notes	lecture-notes	16
Finite simple groups: Lecture 4 — Exceptional groups	lecture-notes	33
On the simple groups of Suzuki and Ree	paper	10
GAP Reference Manual: Groups	documentation	7
GAP Reference Manual: Group Libraries	documentation	11
GAP ClassicalMaximals: Classical Groups and Aschbacher’s Theorem	documentation	1
Character Theory of Finite Groups: Day 4 — The McKay Correspondence	lecture-notes	10
Groups with a p-element acting with a single non-trivial Jordan block on a simple module in characteristic p	paper	19
Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics	paper	3
ATLAS of Finite Group Representations: Sporadic groups	database	82
GroupNames: C₂	database	12
GroupNames: C₄	database	11
GroupNames: C₅	database	12
GroupNames: C₆	database	11
GroupNames: C₂ × C₂	database	11
GroupNames: D₅, order 10	database	11
GroupNames: D₆, order 12	database	12
GroupNames: Dic₃	database	12
GroupNames: Q₁₆	database	11
GroupNames: SL(2,3), binary tetrahedral	database	16
GroupNames: CSU(2,3), binary octahedral	database	16
GroupNames: SL(2,5), binary icosahedral	database	16
GroupNames: GL(3,2) ≅ PSL(2,7)	database	11
GroupNames: He₃	database	10
GroupNames: A₆	database	12
ATLAS: Mathieu group M11	database	4
ATLAS: Mathieu group M12	database	4
ATLAS: Mathieu group M22	database	4
ATLAS: Mathieu group M23	database	4
ATLAS: Mathieu group M24	database	4
ATLAS: First Janko group	database	4
ATLAS: Hall–Janko group	database	4
ATLAS: Third Janko group	database	4
ATLAS: Fourth Janko group	database	4
ATLAS: First Conway group	database	4
ATLAS: Second Conway group	database	4
ATLAS: Third Conway group	database	4
ATLAS: Fischer group Fi22	database	4
ATLAS: Fischer group Fi23	database	4
ATLAS: Fischer simple group Fi24 prime	database	5
ATLAS: Higman–Sims group	database	4
ATLAS: McLaughlin group	database	4
ATLAS: Held group	database	4
ATLAS: Rudvalis group	database	4
ATLAS: Sporadic Suzuki group	database	5
ATLAS: O’Nan group	database	4
ATLAS: Harada–Norton group	database	4
ATLAS: Lyons group	database	4
ATLAS: Thompson group	database	4
ATLAS: Baby Monster group	database	4
ATLAS: Monster group	database	4
ATLAS: Tits group ²F₄(2)′	database	5
Math 210C. Centers of simply connected semisimple groups	lecture-notes	614
Lie Groups and Lie Algebras	lecture-notes	505
Lecture 6: Maximal Root, Exponents, Coxeter Numbers, Dual Representations	lecture-notes	95
Lecture 15: Classification of Real Forms of Semisimple Lie Algebras	lecture-notes	586
Lecture 17: Classification of Connected Compact and Complex Reductive Groups	lecture-notes	134
Lie Groups Beyond an Introduction — Chapter VI: Structure Theory of Semisimple Groups	book	100
Sporadic isogenies to orthogonal groups	lecture-notes	144
The Octonions	paper	6
K-theory and limit-of-discrete-series for the universal cover of SL₂(R)	paper	18
Algebraic Topology	book	13
Etingof et al., Introduction to Representation Theory	lecture-notes	304
GAP Reference Manual, Chapter 73: Maps Concerning Character Tables	documentation	274
Lie Groups and Lie Algebras I	lecture-notes	416
SageMath: Cartan matrices	documentation	416
SageMath: Root system data for type E	documentation	65
SageMath: Root system data for type B	documentation	0
SageMath: Root system data for type C	documentation	26
SageMath: Root system data for type F	documentation	26
SageMath: Root system data for type G	documentation	26
SageMath: Gelfand–Tsetlin patterns	documentation	0
The Real Chevalley Involution	paper	416
Thomas D. Cohen, Center symmetry and area laws	paper	0
SageMath: Littlewood–Richardson Calculator interface	documentation	0
Symmetries of Plane Partitions	paper	0
SageMath: Schur symmetric functions	documentation	0
LieART — A Mathematica Application for Lie Algebras and Representation Theory	paper	0
The Algebra of Grand Unified Theories	paper	112
Brian Conrad, Fundamental Groups of Lie Groups	lecture-notes	112
Efficient Hilbert Series for Effective Theories	paper	0
Hilbert Series for Constructing Lagrangians: expanding the phenomenologist’s toolbox	paper	0
Enumerating the operators of an effective field theory	paper	0
Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry	paper	0
Higher dimension operators in the SM EFT	paper	0
Steven Weinberg, Baryon- and Lepton-Nonconserving Processes	paper	0
Renormalization Group Evolution of the Standard Model Dimension Six Operators III: Gauge Coupling Dependence and Phenomenology	paper	0
Renormalization group evolution of dimension-six baryon number violating operators	paper	0
Baryon Number, Lepton Number, and Operator Dimension in the Standard Model	paper	0

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