Energy representations of gauge groups associated with Riemannian flags

Abstract We construct, given a Riemannian flag on a smooth manifold X and a compact semi-simple Lie group G , a unitary representation of order 1 of the G -valued gauge group, i.e., of the group of G -valued, compactly supported, smooth mappings on X . For dim( X ) ⩾ 2 (with a supplementary condition in the case dim( X ) = 2, we show that this representation is irreducible and that the representations associated to different Riemannian flags are inequivalent. These results appear as extensions of the corresponding ones related to the classical energy representation and its previously introduced generalizations.