Modular Representation Theory
Representations in positive characteristic, blocks, and decomposition matrices.
Modular Representation Theory. Representations in positive characteristic, blocks, and decomposition matrices.
Foundations and canonical references
The standard treatments of modular representation theory approach the subject from complementary angles. Alperin, Modular Representation Theory (1986) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Benson, Representations and Cohomology I (1998) offers an alternative presentation that complements the primary references and is useful for triangulating definitions and proof techniques.
Open methodological questions for modular representation theory include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 1986Modular Representation Theoryalperin-1986
- textbook · supporting · 1998Representations and Cohomology Ibenson-1998
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