This article is cited in 7 papers

Orbits and their closures in the spaces $\mathbb C^{k_1}\otimes\dots\otimes\mathbb C^{k_r}$

P. G. Parfenov

M. V. Lomonosov Moscow State University

Abstract: Natural actions of direct products of general linear groups on tensor products of the corresponding complex linear spaces are considered. Among these actions, all actions with finitely many orbits are distinguished. The main results of the paper are the classification of orbits and the construction of the orbit abutment graphs for all such actions.

UDC: 512.815.4

MSC: Primary 32M05; Secondary 14L24, 14M17, 22E10, 57S25

Received: 18.10.1999

DOI: 10.4213/sm537

 English version: Sbornik: Mathematics, 2001, 192:1, 89–112

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