REPRESENTATION THEORY (M1, Alperin)

Lecture Topic : (Pure Math) REPRESENTATION THEORY (M1, Alperin)

Prerequisites : Finite Group Theory (Sen, M1); Abstract Algebra (Sen, M1);

Recommended Text(s) :

“Groups and Representations”, Graduate Texts in Mathematics (GTM) No. 162, J. L. Alperin & Rowen B. Bell,  Princeton, 1995.

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Lectures and Links :

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Lecture 0  (link)

Ch.0   Preface

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1.   Rudiments of Group Theory

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Lecture 1  (link)

Ch.1   Review

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Lecture 2  (link)

Ch.2   Automorphisms

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Lecture 3  (link)

Ch.3   Group Actions

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2.   The General Linear Group

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Lecture 4 (link)

Ch.4   Basic Structure

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Lecture 5  (link)

Ch.5   Parabolic Subgroups

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Lecture 6  (link)

Ch.6   The Special Linear Groups

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3.   Local Structure

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Lecture 7  (link)

Ch.7   Sylow’s Theorem

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Lecture 8  (link)

Ch.8   Finite p-Groups

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Lecture 9  (link)

Ch.9   The Schur-Zassenhaus Theorem

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4.   Normal Structure

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Lecture 10  (link)

Ch.10   Composition Series

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Lecture 11  (link)

Ch.11   Solvable Groups

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5.   Semisimple Algebras

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Lecture 12  (link)

Ch.12   Modules and Representations

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Lecture 13  (link)

Ch.13   Wedderburn Theory

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6.   Group Representations

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Lecture 14  (link)

Ch.14   Characters

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Lecture 15  (link)

Ch.15   The Character Table

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Lecture 16  (link)

Ch.16   Induction

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Lecture 17  (link)

Appendix : Algebraic Integers and Characters

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