Math 251C - Lie Groups (Spring 2020)

We will cover additional topics in Lie groups and their representations: tensor constructions for representations, classical invariant theory, group actions, flag varieties
There is no single textbook for this course, but you may find some of the following books/papers useful: Here are my typed notes for the course: Notes (last updated 5/24/20)

Homework

Other resources

Lectures

Mar 301.1: Representations
notes | video
Apr 11.1: Representations
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Apr 31.1: Representations
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Apr 61.2: Multiplicity-free actions
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Apr 81.2: Multiplicity-free actions, generic matrices
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Apr 101.2: Multiplicity-free actions, symmetric matrices
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Apr 131.2: Multiplicity-free actions, skew-symmetric matrices
1.3: Schur functors
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Apr 151.4: Symmetric polynomials
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Apr 171.4: Symmetric functions
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Apr 202.1: Symplectic group basics
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Apr 222.2: Multiplicity-free action
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Apr 242.3: Branching problem
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Apr 272.4: Characters of the symplectic group
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Apr 292.4: Characters of the symplectic group
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May 13.1: Orthogonal group basics
3.2: Multiplicity-free action
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May 43.3: Branching problem
3.4: Characters of the orthogonal group
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May 64.1: Projective space
4.2: Grassmannians
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May 84.3: Partial flag varieties
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May 114.4: Borel-Weil theorem
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May 134.5: Symplectic and orthogonal analogues
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May 154.6: Kempf-Weyman collapsing
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May 184.7: Dynkin diagrams
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May 205.1: Schur-Weyl duality
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May 225.2: First fundamental theorem of invariant theory
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5.3: Brauer algebras
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6.1: Clifford algebras
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6.2: Spin groups
notes | video