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Let p be a prime number and F a totally real field. In this article, we obtain a p-adic interpolation of spaces of totally definite quaternionic automorphic forms over F of finite slope, and construct p-adic families of automorphic forms parametrized by affinoid Hecke varieties. Further, as an application to the case where [F : Q] is even, we obtain p-adic analytic families of Hilbert eigenforms having fixed finite slope parametrized by weights. This is an analogue of Coleman's analytic families in [R.F. Coleman, p-Adic Banach spaces and families of modular forms, Invent. Math. 127 (1997) 417-479].

Let f be a primitive form whose weight is greater than 2. Weston [23, Theorem 1] showed that the mod p representation ρ associated to f is irreducible and the deformation problem for ρ is unobstructed for almost all p. The aim of this article is to give a simpler proof of his result in some cases.

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