Lie algebras, Lie groups
[ambient page updated 12 Jun '09]
...
[ home ]
...
[ garrett@math.umn.edu ]
- [ classical homogeneous spaces ]
...
[ updated
02 Nov '06]
...
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 ]
...
[ updated 24 Apr '05]
...
classical groups over R and C, classical cones,
Harish-Chandra and Borel realizations of bounded symmetric domains.
- [ invariant differential operators ]
...
[ updated
15 Mar '06]
...
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 ]
...
[ updated 09 Sep '08]
...
basic representation theory of Lie algebras illustrated for sl(2) and sl(3)
© 1996-2009,
Paul Garrett
...
[ garrett@math.umn.edu
]
[this page is http://www.math.umn.edu/~garrett/m/lie/]
The University of Minnesota explicitly requires that I
state that "The views and opinions expressed in this page are
strictly those of the page author. The contents of this page have not
been reviewed or approved by the University of Minnesota."