ISSN:
1573-0530
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract Let G=KL and g=k+l be Lie group and Lie algebra decompositions. This identifies k o with l *. Any G-invariant function, f, on g *induces by restriction a function f|k o =l *. We prove a formula which says that the integral curve through α∈k o is obtained as b(t)α, where a(t)=exp tξ with ξ=L f (α), $$\left( * \right){\text{ }}a\left( t \right) = b\left( t \right)c\left( t \right)$$ where (*) is the KL decomposition and where L f : g * → g is the Legendre transform. This generalizes a formula of Symes for the generalized Toda lattice.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00419928
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