Lie algebras, Lie groups
[ambient page updated 09 Sep '17]
...
[ home ]
...
[ garrett@math.umn.edu ]
( See also:
[ vignettes ]
...
[ functional analysis ]
...
[ intro to modular forms ]
...
[ representation theory ]
...
[ Lie theory, symmetric spaces ]
...
[ buildings notes ]
...
[ number theory ]
...
[ algebra ]
...
[ complex analysis ]
...
[ real analysis ]
...
[ homological algebra ]
)
- [ matrix exponentiation ]
...
[ updated
15 Jul '10]
...
Convergence of matrix exponentiation via operator norm.
- [ classical homogeneous spaces ]
...
[ updated
25 Sep '10]
...
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 23 Oct '22]
...
classical groups over R and C, classical cones,
Harish-Chandra and Borel realizations of bounded symmetric domains.
- [ invariant differential operators ]
...
[ updated
28 Oct '10]
...
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 26 Oct '17]
...
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.
...
[ garrett@umn.edu ]
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."