Communications in Analysis and Geometry

Volume 17 (2009)

Number 2

A quadratic inequality for sum of co-adjoint orbits

Pages: 265 – 282

DOI: http://dx.doi.org/10.4310/CAG.2009.v17.n2.a4

Authors

Naichung Conan Leung (Department of Mathematics, The Chinese University of Hong Kong)

Xiaowei Wang (Department of Mathematics, The Chinese University of Hong Kong)

Abstract

We obtain an effective lower bound on the distance of thesum of co-adjoint orbits from the origin. Even when thedistance is zero (thus the symplectic quotient is welldefined) our result gives a nontrivial constraint on theseco-adjoint~orbits. In the particular case of unitarygroups, we obtain the quadratic inequality foreigenvalues of Hermitian matrices satisfying\begin{equation*}A+B=C.\end{equation*}This quadratic inequality can be interpreted as the Chern number inequalityfor semi-stable reflexive toric sheaves.

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