18 739 - Theory of Invariants

Institution:

Massachusetts Institute of Technology

Subject:

Description:

Hilbert's finiteness theorem for reductive groups. Properties of the orbits and the orbit space. Classical invariant theory. Hilbert-Mumford-Richardson theorem. Rosenlicht's theorem on the existence of invariants. Matsushima criterion. Richardson's theorem on the principal stabilizer. Chevalley-Luna-Richardson theorem. Linear actions with a non-trivial stabilizer. Polar representations. Methods of the orbit classification. Applications to classical problems of linear algebra. Other topics.

Credits:

3.00

Credit Hours:

Prerequisites:

Prereq: 18.705

Corequisites:

Exclusions:

Level:

Instructional Type:

Lecture

Notes:

Additional Information:

Historical Version(s):

Institution Website:

web.mit.edu/student/

Phone Number:

(617) 253-1000

Regional Accreditation:

New England Association of Schools and Colleges

Calendar System:

Four-one-four plan

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