Weil representations as globally irreducible representations

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The notion of globally irreducible representations of finite groups was introduced by B. H. GROSS, in order to explain new series of Euclidean lattices discovered recently by N. ELKIES and T. SHIODA using Mordell-Weil lattices of elliptic curves. It has been observed by R. Gow and GROSS that irreducible Weil representations of certain finite classical groups lead to globally irreducible representations. In this paper we classify all globally irreducible representations coming from Weil representations of finite classical groups.

Original languageEnglish (US)
Pages (from-to)313-327
Number of pages15
JournalMathematische Nachrichten
StatePublished - 1997
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


  • Globally irreducible representations
  • Integral lattices
  • Weil representations


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