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Localization of valuations and Alesker's irreducibility theorem

2025/10/29 by Georg C. Hofstätter, Hofstätter, Georg C., Jonas Knoerr +1
Mathematics · Computer Science · #Point processes and geometric inequalities #Advanced Differential Equations and Dynamical Systems #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2510.25698

Abstract

We provide a new proof of Alesker's Irreducibility Theorem. We first introduce a new localization technique for polynomial valuations on convex bodies, which we use to independently prove that smooth and translation invariant valuations are representable by integration with respect to the normal cycle. This allows us to reduce the statement to a corresponding result for the representation of \mathfraksl(n) on the space of these differential forms.

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