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Representation Theory

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Author(s): S. Martin, ed. Dexter Chua
Series: Cambridge Mathematical Tripos Part II Lecture Notes
Publisher: University of Cambridge
Year: 2016

Language: English
City: Cambridge
Tags: maths; mathematics; math; advanced; college; university; higher; further; pure; applied; representation; information; coding; code; encoding

Introduction
Group actions
Basic definitions
Complete reducibility and Maschke's theorem
Schur's lemma
Character theory
Proof of orthogonality
Permutation representations
Normal subgroups and lifting
Dual spaces and tensor products of representations
Dual spaces
Tensor products
Powers of characters
Characters of G x H
Symmetric and exterior powers
Tensor algebra
Character ring
Induction and restriction
Frobenius groups
Mackey theory
Integrality in the group algebra
Burnside's theorem
Representations of compact groups
Representations of SU(2)
Representations of SO(3), SU(2) and U(2)
Index