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A converse to the Grace–Walsh–Szegő theorem

Published online by Cambridge University Press:  01 September 2009

PETTER BRÄNDÉN  and
DAVID G. WAGNER
PETTER BRÄNDÉN
Affiliation:
Department of Mathematics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden. e-mail: pbranden@math.kth.se
DAVID G. WAGNER
Affiliation:
Department of Combinatorics and Optimization, University of Waterloo, Ontario, CanadaN2L 3G1. e-mail: dgwagner@math.waterloo.ca
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Abstract

We prove that the symmetrizer of a permutation group preserves stability if and only if the group is orbit homogeneous. A consequence is that the hypothesis of permutation invariance in the Grace–Walsh–Szegő Coincidence Theorem cannot be relaxed. In the process we obtain a new characterization of the Grace-like polynomials, introduced by D. Ruelle, and prove that the class of such polynomials can be endowed with a natural multiplication.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 147 , Issue 2 , September 2009 , pp. 447 - 453
Copyright
Copyright © Cambridge Philosophical Society 2009

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References

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