Abstract
Let p be an odd prime. It is known that the symplectic group Sp2n(p) has two (algebraically conjugate) irreducible representations of degree (pn + l)/2 realized over Q(p), where e = (-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.
Original language | English (US) |
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Pages (from-to) | 2101-2139 |
Number of pages | 39 |
Journal | Transactions of the American Mathematical Society |
Volume | 351 |
Issue number | 5 |
DOIs | |
State | Published - 1999 |
Externally published | Yes |
Keywords
- Finite symplectic group
- Integral lattice
- Linear code
- Maslov index
- P-modular lattice
- Self-dual code
- Unimodular lattice
- Weil representation
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics