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Mat. Sb., 1992, Volume 183, Number 11, Pages 99–116 (Mi msb1091)  

This article is cited in 2 scientific papers (total in 2 papers)

Basic spin representations of alternating groups, Gow lattices, and Barnes–Wall lattices

Pham Huu Tiep


Abstract: In a recent paper, R. Gow showed that in certain cases the basic spin representations of the group $2\mathfrak{A}_n$ (of degree $2^{[\frac{n}{2}]-1}$) can be rational. In such cases, the $2\mathfrak{A}_n$-invariant lattices $\Lambda$ in the corresponding rational module have many interesting properties. In the present paper all possibilities are found for the groups $G=\operatorname{Aut}(\Lambda)$. Also, a conjecture of Gow is proved: For $n=8k$, $ k\in\mathbb{N}$, there is among the $2\mathfrak{A}_n$-invariant lattices the even unimodular Barnes–Wall lattice $BW_{2^{4k-1}}$. At the same time, the rationality of the basic spin representation of $ 2\mathfrak{A}_{8k}$ and the reducibility of $\Lambda/2\Lambda$ as a $2\mathfrak{A}_{8k}$-module are proved.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1994, 77:2, 351–365

Bibliographic databases:

UDC: 512
MSC: 20C30, 11H56
Received: 18.06.1991

Citation: Pham Huu Tiep, “Basic spin representations of alternating groups, Gow lattices, and Barnes–Wall lattices”, Mat. Sb., 183:11 (1992), 99–116; Russian Acad. Sci. Sb. Math., 77:2 (1994), 351–365

Citation in format AMSBIB
\Bibitem{Pha92}
\by Pham Huu Tiep
\paper Basic spin representations of alternating groups, Gow lattices, and Barnes--Wall lattices
\jour Mat. Sb.
\yr 1992
\vol 183
\issue 11
\pages 99--116
\mathnet{http://mi.mathnet.ru/msb1091}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1208216}
\zmath{https://zbmath.org/?q=an:0813.20013}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1994SbMat..77..351K}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1994
\vol 77
\issue 2
\pages 351--365
\crossref{https://doi.org/10.1070/SM1994v077n02ABEH003445}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1994NF83500007}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. K. S. Abdukhalikov, “Integral lattices associated with a finite affine group”, Russian Acad. Sci. Sb. Math., 83:2 (1995), 431–443  mathnet  crossref  mathscinet  zmath  isi
    2. Pham Huu Tiep, “Weil Representations as Globally Irreducible Representations”, Math Nachr, 184:1 (1997), 313  crossref  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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