00311 - Isometric Actions of Lie Groups and Invariants.pdf

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tgbook.dvi

Polynomial Invariant Theory

Invariant Theory of Compact Lie Groups

Transformation Groups

Proper Actions

Riemannian Gmanifolds

Riemannian Submersions

Sections

The Generalized Weyl Group of a Section

Basic Dierential Forms

Basic versus equivariant cohomology

Let Sn denote the space of symmetric n n matrices with entries in R and

B with equals the S

orbit through B where S

phic to R

for all X

TakeanA in For any X on that is for anyskewsymmetric Xlet

XA AX

for all H Sn

f f as above is possible due to the following theorem by

as generators of R

R

S

J

dx

The mapping is a local dieomorphism on the open set U n J

x

where c R

g for all S

h C

Claim Let

d

j

C

d

dx

C

det

C

j U and