Title: Representation Theory

Description: An introduction to representation theory, with a focus on explicit examples. Representations of finite groups (in characteristic zero), especially symmetric and alternating groups. Representation theory of compact Lie groups and semisimple Lie algebras (which may also be covered in MAT 552). Representations of classical groups, esp. GL(n) and orthogonal groups. Schur-Weil duality for representations of S_n and GL(n), Young diagrams. Other possible topics include spin representations and Clifford algebras, representations of exceptional groups, applications to physics (e.g. hydrogen atom, spin, quarks), or an introduction to invariant theory.

Offered: Fall

Prerequisite: MAT 535

Credits: 3

Textbook:

• Sample textbooks:
  W. Fulton and J. Harris, Representation Theory: A First Course
  A. Kirillov, Introduction to Lie Groups and Lie Algebras
  T. Brocker, Representations of compact Lie groups
  P. Etingof et al, Introduction to representation theory
  G. Heckman, Lie Algebras in Mathematics and Physics
  

   Note: Subject to change - do not buy before confirming with the course instructor

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