Lecture 2- Modular Representations and Brauer Characters
Lecture 2- Modular Representations and Brauer Characters
Introduces modular systems (K, O, k), defines p-regular vs p-singular elements, and develops Brauer characters (defined on p-regular classes) with the Brauer–Nesbitt theorem. Explains reduction mod p, the decomposition matrix D linking ordinary and Brauer characters, and that the number of Brauer irreducibles equals the number of p-regular conjugacy classes. Worked examples include S₃ at p=3 and the kernel phenomenon in passing from ordinary to modular characters; a preview points to Frobenius actions and field-of-definition issues next.
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reduction mod p, modular representation theory, kernel/nullspace, p-regular/p-singular, S₃ example, Brauer characters, decomposition matrix, Brauer–Nesbitt
reduction mod p, modular representation theory, kernel/nullspace, p-regular/p-singular, S₃ example, Brauer characters, decomposition matrix, Brauer–Nesbitt
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