Abstract
A “system of coordinates” on a set Λ of selfdual lattices in a two-dimensionalp-adic symplectic space (V,ℬ) is suggested. A unitary irreducible representation of the Heisenberg group of the space (V,ℬ) depending on a lattice ℒ∈Λ (an analogue of the Cartier representation) is constructed and its properties are investigated. By the use of such representations for three different lattices ℒ∈Λ one defines the Maslov index μ=μ(ℒ1,ℒ2,ℒ3) of a triple of lattices. Properties of the index μ are investigated and values of μ in coordinates for different triples of lattices are calculated.
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