ncatlab.org
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nLab is a collaborative online wiki of advanced mathematics and related fields, with extensive pages on category theory, higher categories, algebra, and representation theory. It offers rigorously written articles, definitions, and cross-referenced notes (including irreducible representations) with links to relevant literature and concepts.
More resources on Irreducible Representations
John Baez Rep Theory
Intro article with irreducibles
Etingof Representation Theory Notes
Free PDF notes on rep theory including irreducibles
mathworld.wolfram.com
MathWorld is Wolfram's comprehensive online math encyclopedia featuring concise, well-structured articles on mathematical concepts, definitions, theorems, and examples. It covers topics across mathematics, including group theory and representation theory (e.g., irreducible representations), with formulas, diagrams, and references.
ocw.mit.edu
MIT OpenCourseWare provides free, openly licensed MIT course materials—lectures, notes, assignments, and exams. It includes math courses on representation theory where you can learn about irreducible representations.