In this paper we begin to explore the relation between question of unitarizability classical p-adic groups, and Arthur packets, starting from Tadi? (Mem Am Math Soc 2020, appear).

We formulate a conjectural p-adic analogue of Borel’s theorem relating regulators for higher K-groups of number fields to special values of the corresponding ζ-functions, using syntomic regulators and p-adic L-functions. We also formulate a corresponding conjecture for Artin motives, and state a conjecture about the precise relation between the p-adic and classical situations. Parts of the conj...

Given a quaternionic form $$\textrm{G}$$ of p-adic classical group (p odd) we classify all cuspidal irreducible representations with coefficients in an algebraically closed field characteristic different from p. We prove two theorems: At first: Every representation is induced type, i.e. certain compact open subgroup , constructed $$\beta $$ -extension and finite group. Secondly show that intert...

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...

A brief review of p-adic and adelic cosmology is presented. In particular, p-adic and adelic aspects of gravity, classical cosmology, quantum mechanics, quantum cosmology and the wave function of the universe are considered. p-Adic worlds made of p-adic matters, which are different from real world of ordinary matter, are introduced. Real world and p-adic worlds make the universe as a whole. p-A...