Introduction to Representation Theory, Lie Theory,
Harmonic Analysis
by examples
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Math 8300, 201415, (Fall: 207 Vincent Hall) 1:252:15, MWF
 Representations of
finite abelian groups
[ updated
08:10, Oct 04, 2014]
 Representations of
dihedral groups
[ updated
08:10, Oct 12, 2014]
 Representations of finite 2x2 mirabolic subgroups
 Generalities

Representations of GL_{2} over a finite field
[ updated
11:11, Nov 24, 2014]

Representations of finite Heisenberg groups, theta
correspondences on finite SO(2)xSL_{2}
[ updated
11:11, Nov 24, 2014]
 Representations of finite Heisenberg groups
 Finite SegalShaleWeil (oscillator) representations
 SegalShaleWeil (oscillator) representation construction of cuspidal
representations
for SL_{2}(F_{q})
 ...
 Representations of the circle group T

unitary repns of topological groups
[ updated
14:08, Aug 03, 2014]
 Representations of the rotation group SO(3) of the
twosphere S^{2} and spherical
harmonics
 Verma modules of sl_{2},
highestweight representations
 Highestweight classification of irreducibles for unitary groups
U(n)
 Finitedimensional representations of matrix
groups SL_{2}(R)
and SL_{2}(C) and their Lie
algebras sl_{2}(R)
and sl_{2}(C)
 Quantum harmonic oscillator,
oscillator/SegalShaleWeil representation of
the Lie algebra sl_{2}(R)
 Weyl character formula for unitary groups U(n)
 Unitary representations of SL_{2}(R)
and SL_{2}(C), principal
series representations, holomorphic discrete series

Intertwining operators among principal series for
SL_{2}(R)
[ updated
16:01, Jan 03, 2009]
 Representations of profinite groups: padic group GL_{2}(Z_{p})
 Representations of padic
groups GL_{2}(Q_{p})
principal series, supercuspidal
representations
 The tree attached
to SL_{2}(Q_{p})
and the buildings attached
to SL_{n}(Q_{p})
 BorelCasselmanMatsumoto theorem on representations with
Iwahorifixed vectors

StonevonNeumann theorem for real and padic Heisenberg groups
[ updated
13:04, Apr 22, 2015]
 SegalShaleWeil repns, theta/Howe correspondences, liftings of automorphic forms
 ...
More later.
Unless explicitly noted otherwise, everything here, work
by Paul Garrett, is licensed
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Commons Attribution 3.0
Unported License.
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[ garrett@math.umn.edu ]
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