Representation Theory Epiphany

Abstract.

These lecture notes are for the Epiphany term of the Representation theory module. These notes are adapted from those written by Jack Shotton who, in turn, based his on those by Jens Funke from a previous iteration of this course. Those are based on multiple sources, especially [1] and [3]. Here is a brief rundown of a few references you could look at:

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  We rely a lot on “Fulton and Harris”: [1]. This book takes the point of view that examples should come before theory. It has lots of good exercises. It would be particularly useful for the $\mathfrak{sl}_{3,\mathbb{C}}$-theory. It doesn’t discuss Lie groups (as opposed to algebras) much.

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  Kosmann–Schwarzbach’s book [3] is a relative short source, and is good for its concrete discussion of representations Lie groups.

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  Lastly ones can also consult Hall, [2], for the theory of linear Lie groups, Lie algebras and representations. It is complete yet readable.