Characters of Finite Abelian Groups
by Keith Conrad · University of Connecticut
Expository note treating characters of finite abelian groups as an analogue of Fourier analysis: character tables for cyclic groups, the dual group, orthogonality relations, and applications to Dirichlet's theorem and the discrete Fourier transform.
More resources on Character Theory
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
Representations and Characters of Groups (2nd Edition)
Builds the theory from linear algebra through Maschke's theorem, Schur's lemma, characters and orthogonality relations, with character tables computed explicitly for many small groups. Second edition adds chapters on GL(2,q) and permutation characters, plus full exercise solutions.
Cambridge Part II Representation Theory — Lecture Notes
Full lecture notes for Cambridge Part II Representation Theory (S. Martin, Lent 2016). Chapters cover character theory, a proof of the orthogonality relations, permutation characters, induction and restriction, Mackey theory, and Burnside's p^a q^b theorem.
CTblLib: The GAP Character Table Library
Character theory is one of the few areas where hands-on computation genuinely changes understanding: decomposing characters, checking orthogonality and inducing from subgroups become concrete once you can run them. The tutorial chapter makes it usable, not just a reference dump. GAP add-on package shipping ordinary and modular character tables drawn from the ATLAS of Finite Groups and other sources. The manual covers the tutorial, user interface, table construction functions and interfaces to other character-table data formats.
ATLAS of Finite Group Representations, Version 3
Primary database of explicit matrix and permutation representations for 716 finite simple groups and related groups, totalling 5,215 representations, with generators, standard presentations, black-box algorithms and links to ATLAS character table data.
Character Theory of Finite Groups
Isaacs develops the character theory of finite groups from scratch: orthogonality relations, class functions, induced characters and Frobenius reciprocity, Brauer's theorems, and Burnside's p^a q^b theorem. Includes roughly 300 exercises and full proofs throughout.