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Mat. Zametki, 2012, Volume 92, Issue 4, Pages 483–496 (Mi mz9073)  

This article is cited in 1 scientific paper (total in 1 paper)

Simple Modules of Exceptional Groups with Normal Closures of Maximal Torus Orbits

I. I. Bogdanova, K. G. Kuyumzhiyanb

a Moscow Institute of Physics and Technology
b National Research University "Higher School of Economics"

Abstract: Let $G$ be an exceptional simple algebraic group, and let $T$ be a maximal torus in $G$. In this paper, for every such $G$, we find all simple rational $G$-modules $V$ with the following property: for every vector $v\in V$, the closure of its $T$-orbit is a normal affine variety. To solve this problem, we use a combinatorial criterion of normality formulated in terms of weights of simple $G$-modules. This paper continues the works of the second author in which the same problem was solved for classical linear groups.

Keywords: variety, normality, irreducible representation, exceptional group, maximal torus, weight decomposition

DOI: https://doi.org/10.4213/mzm9073

Full text: PDF file (556 kB)
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English version:
Mathematical Notes, 2012, 92:4, 445–457

Bibliographic databases:

UDC: 512.743.7
Received: 09.09.2011

Citation: I. I. Bogdanov, K. G. Kuyumzhiyan, “Simple Modules of Exceptional Groups with Normal Closures of Maximal Torus Orbits”, Mat. Zametki, 92:4 (2012), 483–496; Math. Notes, 92:4 (2012), 445–457

Citation in format AMSBIB
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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. G. Kuyumzhiyan, “Simple modules of classical linear groups with normal closures of maximal torus orbits”, Siberian Math. J., 53:6 (2012), 1089–1104  mathnet  crossref  mathscinet  isi  elib  elib
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