Stony Brook University 3 credits MAT
[will alternate with MAT 544 ] 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. Sample textbooks: 3 credits Prerequisite: MAT 535 . Grading Letter graded (A, A-, B+, etc.)
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