Symplectic Group Lattices
نویسنده
چکیده
Let p be an odd prime. It is known that the symplectic group Sp2n(p) has two (algebraically conjugate) irreducible representations of degree (pn +1)/2 realized over Q(√ p), where = (−1)(p−1)/2. We study the integral lattices related to these representations for the case pn ≡ 1 mod 4. (The case pn ≡ 3 mod 4 has been considered in a previous paper.) We show that the class of invariant lattices contains either unimodular or p-modular lattices. These lattices are explicitly constructed and classified. Gram matrices of the lattices are given, using a discrete analogue of Maslov index.
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تاریخ انتشار 1999