Abstract:
This paper deals with positive definite integral lattices of dimension $\operatorname{Card}(V)-1$ associated with a finite affine group $V\cdot\operatorname{GL}(V)$ (and some of its subgroups). The invariant sublattices are described to within similarity. Duality in the class of invariant lattices is studied. The unimodular lattices are distinguished.
\Bibitem{Abd94}
\by K.~S.~Abdukhalikov
\paper Integral lattices associated with a~finite affine group
\jour Russian Acad. Sci. Sb. Math.
\yr 1995
\vol 83
\issue 2
\pages 431--443
\mathnet{http://mi.mathnet.ru/eng/sm944}
\crossref{https://doi.org/10.1070/SM1995v083n02ABEH003599}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1317296}
\zmath{https://zbmath.org/?q=an:0843.11031}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995TQ10300009}
Linking options:
https://www.mathnet.ru/eng/sm944
https://doi.org/10.1070/SM1995v083n02ABEH003599
https://www.mathnet.ru/eng/sm/v185/i12/p3
This publication is cited in the following 3 articles:
K. Abdukhalikov, “The Permutation Modules for Finite (Affine) General Linear Groups”, Journal of Mathematical Sciences (New York), 131:5 (2005), 5867
K. S. Abdukhalikov, “Automorphism groups of invariant lattices in the Steinberg module of groups of Lie type of odd characteristic”, Sb. Math., 189:9 (1998), 1273–1294
K. S. Abdukhalikov, “Modular permutation representations of $\operatorname {PSL}(n,p)$”, Sb. Math., 188:8 (1997), 1107–1117
Citation in format AMSBIB
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