Universal subspaces for compact Lie groupsReport as inadecuate



 Universal subspaces for compact Lie groups


Universal subspaces for compact Lie groups - Download this document for free, or read online. Document in PDF available to download.

Download or read this book online for free in PDF: Universal subspaces for compact Lie groups
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 Un, Spn, and SOn in the space of $n\times n$ matrices over C, H, and R, respectively. In particular, we obtain an interesting generalization of Schurs triangularization theorem.



Author: Jinpeng An; Dragomir Z. Djokovic

Source: https://archive.org/







Related documents