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Universal subspaces for compact Lie groups
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Published/Copyright:
October 21, 2010
Abstract
For a representation of a connected compact Lie group G in a finite dimensional real vector space 𝒰 and a subspace 𝒱 of 𝒰, invariant under a maximal torus of G, we obtain a sufficient condition for 𝒱 to meet all G-orbits in 𝒰, which is also necessary in certain cases. The proof makes use of the cohomology of flag manifolds and the invariant theory of Weyl groups. Then we apply our condition to the conjugation representations of U(n), Sp(n), and SO(n) in the space of n × n matrices over 
, 
, and 
, respectively. In particular, we obtain an interesting generalization of Schur's triangularization theorem.
Received: 2009-04-23
Revised: 2009-08-23
Published Online: 2010-10-21
Published in Print: 2010-October
© Walter de Gruyter Berlin · New York 2010
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Articles in the same Issue
- The asymptotic formulae in Waring's problem for cubes
- Analytic Besov spaces and Hardy-type inequalities in tube domains over symmetric cones
- Algebras of fractions and strict Positivstellensätze for ∗-algebras
- Adiabatic limit, Bismut-Freed connection, and the real analytic torsion form
- Resolutions for representations of reductive p-adic groups via their buildings
- Universal subspaces for compact Lie groups
- Sur l'inégalité de Turán-Kubilius friable
