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Ramified Satake isomorphisms for strongly parabolic characters

Ramified Satake isomorphisms for strongly parabolic characters

For certain characters of the compact maximal torus of a reductive p -adic group, which we call strongly parabolic characters, we prove Satake-type isomorphisms. Our results generalize those of Satake, Howe, Bushnell and Kutzko, and Roche.