This article is cited in 1 paper

Simple modules of classical linear groups with normal closures of maximal torus orbits

K. G. Kuyumzhiyan<sup>ab

a</sup> Independent University of Moscow and Poncelet Laboratory (UMI 2615 of CNRS), Moscow, Russia
^b Higher School of Economics, Laboratory of algebraic geometry and its applications, Moscow, Russia

Abstract: Let $T$ be a maximal torus in a classical linear group $G$. In this paper we find all simple rational $G$-modules $V$ such that for each vector $\mathbf v\in V$ the closure of the $T$-orbit of $\mathbf v$ is a normal affine variety. For every $G$-module without this property we present a $T$-orbit with nonnormal closure. To solve this problem, we use a combinatorial criterion of normality which is formulated in terms of the set of weights of a simple $G$-module. The same problem for $G=SL(n)$ was solved by the author earlier.

Keywords: toric variety, normality, irreducible representation, classical root system, weight decomposition.

UDC: 512.743.7

Received: 21.07.2011

 English version: Siberian Mathematical Journal, 2012, 53:6, 1089–1104

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