Symplectic matrices with predetermined left eigenvalues

Abstract

We prove that given four arbitrary quaternion numbers of norm 1 there always exists a $2\times 2$ symplectic matrix for which those numbers are left eigenvalues. The proof is constructive. An application to the LS category of Lie groups is given.

7 pages

References in corpus (2)

• On the Lusternik-Schnirelmann category of symmetric spaces of classical type
• Trace map, Cayley transform and LS category of Lie groups