p-adic Heisenberg group and Maslov index |
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Authors: | E I Zelenov |
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Institution: | (1) Steklov Mathematical Institute, Vavilov str. 42, GSP-1, 117966 Moscow, Russia |
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Abstract: | A system of coordinates on a set of selfdual lattices in a two-dimensionalp-adic symplectic space (V,) is suggested. A unitary irreducible representation of the Heisenberg group of the space (V,) depending on a lattice (an analogue of the Cartier representation) is constructed and its properties are investigated. By the use of such representations for three different lattices one defines the Maslov index =(1,2,3) of a triple of lattices. Properties of the index are investigated and values of in coordinates for different triples of lattices are calculated. |
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