Lie algebras, Lie groups
[ambient page updated 28 Mar '08]
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[ garrett@math.umn.edu ]
2006-07 course: Math 8271-72, MWF 11:15 in Vincent Hall 364
(Note room change!)
Course notes to appear...
Some things that will be revised and incorporated into course
notes:
- [ classical homogeneous spaces ]
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[ updated
02 Nov '06]
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The fundamental examples: (special) orthogonal groups versus rotations
of spheres, indefinite orthogonal or unitary groups as automorphisms
of (solid) real or complex balls, linear groups acting on projective
spaces and Grassmannians and flag varieties, etc.
- [ classical groups and classical
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[ updated 24 Apr '05]
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classical cones, classical groups over R and C,
Harish-Chandra and Borel realizations of bounded symmetric domains.
- [ invariant differential operators ]
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[ updated
15 Mar '06]
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Invariant Laplacians arising from Casimir operators, the basic
two-sided-invariant element of the universal enveloping
algebra. Coordinate-free description, with (thus!) easy computations
on the upper half-plane, etc.
- [ Verma modules, complete
reducibility, Harish-Chandra isomorphisms, ]
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[ updated 14 Sep '06]
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basic representation theory of Lie algebras illustrated for sl(2) and sl(3)
© 1996-2008,
Paul Garrett
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[ garrett@math.umn.edu
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[this page is http://www.math.umn.edu/~garrett/m/lie/]
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