Lie algebras, Lie groups
[ambient page updated 24 Jul '11]
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[ home ]
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[ garrett@math.umn.edu ]
See also
[vignettes],
[functional analysis],
[intro mfms],
[algebra].
- [ matrix exponentiation ]
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[ updated
15 Jul '10]
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Convergence of matrix exponentiation via operator norm.
- [ classical homogeneous spaces ]
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[ updated
25 Sep '10]
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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, domains,
cones ]
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[ updated 22 Sep '10]
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classical groups over R and C, classical cones,
Harish-Chandra and Borel realizations of bounded symmetric domains.
- [ invariant differential operators ]
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[ updated
28 Oct '10]
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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 09 Sep '08]
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basic representation theory of Lie algebras illustrated for sl(2) and sl(3)
© 1996-2012, Creative Commons license,
This work
by Paul Garrett is licensed
under a Creative
Commons Attribution 3.0
Unported License.
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[ garrett@math.umn.edu ]
[this page is http://www.math.umn.edu/~garrett/m/lie/]
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