Theorems of Carathéodory, Minkowski-Weyl, and Gordan up to Symmetry

Abstract

In this paper we extend three classical and fundamental results in polyhedral geometry, namely, Carath\'{e}odory's theorem, the Minkowski-Weyl theorem, and Gordan's lemma to infinite dimensional spaces, in which considered cones and monoids are invariant under actions of symmetric groups.