Note on the decomposition of states
Bull. Korean Math. Soc. 2018 Vol. 55, No. 4, 1221-1230
Published online July 31, 2018
Donghoon Hyeon, Jaekwang Kim
Seoul National University, POSTECH
Abstract : 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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