Abstract
A representation ρ of a group G in a finite dimensional vector space V over a local field K is said to have regular reduction if for some G-stable OK-lattice Λ, the Jordan-Hölder constituents of the reduction of Λ modulo the maximal ideal mK are pairwise inequivalent.For irreducible representations with regular reduction, we prove a formula for the class number (the number of stable lattices up to homothety) of the base change ρ⊗KE for any totally ramified extension E/K. This is inspired by Iwasawa's theory of Zp-extensions. We also deduce some (irreducibility) properties of such a representation and its Schur algebra.
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