Symplectic group lattices

Rudolf Scharlau, Pham Huu Tiep

Research output: Contribution to journalArticle

3 Scopus citations

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 languageEnglish (US)
Pages (from-to)2101-2139
Number of pages39
JournalTransactions of the American Mathematical Society
Volume351
Issue number5
StatePublished - Dec 1 1999

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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

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