Bulletin of the
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Bull. Korean Math. Soc. 2018; 55(4): 1221-1230

Online first article June 19, 2018      Printed July 31, 2018

https://doi.org/10.4134/BKMS.b170704

Copyright © The Korean Mathematical Society.

Note on the decomposition of states

Donghoon Hyeon, Jaekwang Kim

Seoul National University, POSTECH

Abstract

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We derive a sharp decomposition formula for the state polytope of the Hilbert point and the Hilbert-Mumford index of reducible varieties by using the decomposition of characters and basic convex geometry. This proof captures the essence of the decomposition of the state polytopes in general, and considerably simplifies an earlier proof by the authors which uses a careful analysis of initial ideals of reducible varieties.

Keywords: geometric invariant theory, state polytope

MSC numbers: 14L24

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