Relation between the irreducible representations of Lie algebras and the irreducible representations of $p$-groups

A. V. Matveev

M. V. Lomonosov Moscow State University

Abstract: A proof is given of a theorem stating that there is a correspondence between the irreducible complex representations of a finite $p$-group and the irreducible representations of its associated nilpotent Lie algebra over a field of characteristic $p$. As a corollary it is found that the sets of degrees of the irreducible representations are the same.

UDC: 512

MSC: Primary 20D15; Secondary 17B50, 20C15, 20F40

Received: 23.11.1995

DOI: 10.4213/sm146

 English version: Sbornik: Mathematics, 1996, 187:7, 1039–1043

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