nLab: Representation Theory
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The nLab wiki entry on representation theory, written from a category-theoretic viewpoint. It frames representations as functors and modules, links to related notions such as characters, Tannaka duality, and geometric representation theory, and lists key references for further study.
More resources on Group Representations
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.
Etingof's Introduction to Representation Theory
Free lecture notes by Pavel Etingof and co-authors from MIT, introducing representations of algebras, finite groups, quivers, and Lie algebras, with many exercises. Readers learn character theory, Schur-Weyl duality, and Gabriel's theorem, assuming a solid linear algebra and abstract algebra background.
Applied Geometric Algebra (MIT RES.8-001)
Typeset 1976 lecture notes (11 chapters, about 110 pages) with problems, applying group theory and geometric algebra to physics: rotations, Lorentz transformations, spinors, and the unifying role of symmetry in classical, relativistic and quantum mechanics. Builds geometric intuition for advanced mathematical tools.
Introduction to Representation Theory (MIT 18.712)
Representations of finite groups, Lie algebras, associative algebras and quivers, with character theory and basic category theory. The notes form a full open textbook with exercises, alongside problem sets, building the algebraic tools for studying symmetry in linear spaces.
Representation Theory: A First Course
Graduate textbook (Springer GTM 129) that builds representation theory from finite groups through Lie groups and Lie algebras, emphasizing worked examples. Readers learn character theory, Weyl's construction, and the classification of complex semisimple Lie algebras and their representations.
Representations and Characters of Groups
Undergraduate textbook on representations of finite groups over the complex numbers, requiring only basic group theory and linear algebra. Readers learn Maschke's theorem, character tables, orthogonality relations, induced characters, and applications such as Burnside's paqb theorem.