Sources and component terms

The lessons were written and self-checked by GPT-6.1 Sol (OpenAI), using the Ultra setting in Codex. Each lesson names its mathematical references and states its prerequisite imports.

The independently authored text and course code are dedicated under CC0 1.0. One explicitly marked component has different terms: the first kernel-expansion proof paragraph and its displayed series in Lesson 15, Lemma 1.2, are adapted from Darij Grinberg and Victor Reiner, Hopf Algebras in Combinatorics, Proposition 2.5.15 and proof, pp. 64–66, July 27, 2020 text with minor corrections dated September 6, 2026, under CC BY 4.0. The AI adaptation uses finite alphabets first, the lesson's notation, and explicit degreewise specialization. The following duality proof and later character arguments are independently authored. Preserve the credit and indicate further changes when reusing the adapted component.

Peter Webb's author prepublication draft, February 23, 2016, provides additional reading: row orthogonality and multiplicities at printed pp. 28–31, and adjunctions, transitivity and projection at pp. 58–60. It is used for comparison; an open adaptation license has not been established. The arXiv lecture notes by Pavel Etingof, Oleg Golberg, Sebastian Hensel, Tiankai Liu, Alex Schwendner, Dmitry Vaintrob and Elena Yudovina give induction and Frobenius reciprocity at physical pp. 55–56 of the 108-page edition. Its header identifies arXiv:0901.0827v5, February 1, 2011, and its title page carries November 26, 2024. The course uses the checked notes for independently expressed proof comparison; the notes retain their own rights.

The full signed, integer Brauer theorem and its local induction argument are proved in Lesson 11. Sylow existence and the cyclotomic fixed-field fact are proved in Lesson 5. References, bibliography pages and HTTP success alone are not proof providers. The proof index links the exact course statements, arguments and earlier dependencies.

Source component identities and the 17-lesson source dispositions give versions, source hashes and the boundaries of reuse. Other references retain their own rights; none of the reference PDFs is redistributed here.

The mathematical reader uses MathJax 3.2.2, whose JavaScript is under the Apache License 2.0. Its fonts retain the upstream component terms, including SIL Open Font License 1.1. The shared site's assets/mathjax/LICENSE and assets/mathjax/FONT-LICENSES.txt retain those notices. The vendored Markdown renderer and this course's build wrapper are CC0; their source and a record of their origin and changes are included under tools/.

Proof routes and references

The elementary group and matrix tools are proved in Lessons 3 and 5. The Young-symmetrizer and Schur–Weyl arguments are compared with Caroline Gruson and Vera Serganova, A Journey Through Representation Theory: From Finite Groups to Quivers via Algebras, Springer, 2018, Chapters 2 and 6. The symmetric-function arguments are compared with Grinberg–Reiner and Stembridge; the branching comparison uses Vershik–Okounkov, arXiv:math/0503040v3 (April 20, 2005). Each lesson supplies its course arguments and exact reference locators. The arithmetic aside in Lesson 12 names its number-theory providers and records the Hecke analytic text still absent from the selected reader.