Subgroups of the unitary group over a dyadic local field

Abstract

Let K/k be an unramified quadratic extension of a dyadic local field of characteristic ≠2. In this paper there is studied the lattice of subgroups of the classical unitary group U(n, K), containing the subgroup D of diagonal unitary matrices. The pronormality of the subgroup D in the group U(n, K) is proved and a constructive description is obtained of its unique fan. Analogous results are formulated for the “nonclassical” unitary group U− (n, K) corresponding to a Hermitian form with matrix diag (1,...,1, π) (π is a prime element of the field k).