Here we consider finite-dimensional vector spaces and linear operators on them. Some of the basic ingredients will be motivated by ∗-algebras of linear transformations on inner product spaces, as in [Arv, Dou]. In particular, let us note that in the theory of C and Von Neumann algebras, the “double commutant” of a ∗-algebra is a kind of basic closure of the algebra. A special case concerns alge...

A result of Chai–Faltings on Satake parameters of Siegel cusp forms together with the classification of unitary, unramified, irreducible, admissible representations of GSp4 over a p-adic field, imply that the local components of the automorphic representation of GSp4 attached to a cuspidal Siegel eigenform of degree 2 must lie in certain families. Applications include estimates on Hecke eigenva...

There exists an infinite family of p-compact groups whose Weyl groups correspond to the finite p-adic pseudoreflection groups G(q, r, n) of family 2a in the Clark-Ewing list. In this paper we study these p-compact groups. In particular, we construct an analog of the classical Whitney sum map, a family of monomorphisms and a spherical fibration which produces an analog of the classical J-homomor...