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The Potts model representation and a Robinson–Schensted correspondence for the partition algebra

Published online by Cambridge University Press:  04 December 2007

P. P. MARTIN  and
G. ROLLET
P. P. MARTIN
Affiliation:
Department of Mathematics, City University, Northampton Square, ECIV OHB, London UK
G. ROLLET
Affiliation:
Department of Mathematics, City University, Northampton Square, ECIV OHB, London UK
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Abstract

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We construct a correspondence between the set of partitions of a finite set M and the set of pairs of walks to the same vertex on a graph giving the Bratteli diagram of the partition algebra on M. This is the precise analogue of the correspondence between the set of permutations of a finite set and the set of pairs of Young tableaux of the same shape, called the Robinson–Schensted correspondence.

Keywords

Potts modelinvariant theoryRobinson–Schensted correspondencepartitions of sets.
Type
Research Article
Information
Compositio Mathematica , Volume 112 , Issue 2 , June 1998 , pp. 237 - 254
Copyright
© 1998 Kluwer Academic Publishers