## Lie algebras, Lie groups

[ambient page * updated * 09 Sep '17]
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[* garrett@math.umn.edu *]
(* See also: *
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[ intro to modular forms ]
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[ Lie theory, symmetric spaces ]
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- [ 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 * 08 Jun '18]
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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 * 26 Oct '17]
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basic representation theory of Lie algebras illustrated for sl(2) and sl(3)

Unless explicitly noted otherwise, everything here, work
by Paul Garrett, is licensed
under a Creative
Commons Attribution 3.0
Unported License.
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[* garrett@math.umn.edu *]

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