Abstract
We consider the Hecke algebra of a profinite group G and establish relation between its dual (the algebra of distributions) and the complete group algebra of G. There are p–adic analogs of these notions arising as p–adic rationalizations in the study of quasirational presentations. Using results on representations of finite p–groups over Qp (p-adic numbers) we prove a p–adic analog of the Ritter–Segal theorem and study the only 4–dimensional, primitive, faithful, irreducible representation of the quaternion group of order 16 over a quadratic extension of the field of 2–adic numbers.
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