Dual pairs for matrix groups

Skerritt Paul; Vizman Cornelia

doi:10.3934/jgm.2019014

Article Contents

2019, Volume 11, Issue 2: 255-275. Doi: 10.3934/jgm.2019014

This issue Previous Article Dispersive Lamb systems Next Article Riemannian cubics and elastica in the manifold

$ \operatorname{SPD}(n) $

of all

$ n\times n $

symmetric positive-definite matrices

Dual pairs for matrix groups

Skerritt Paul^1, , and
Vizman Cornelia^2,

1.
Department of Mathematics, University of Surrey, Guildford GU2 7XH, United Kingdom
2.
Department of Mathematics, West University of Timişoara, RO–300223 Timişoara, Romania

^* Corresponding author
^* Corresponding author

Received: March 31, 2018

Revised: February 28, 2019

Published: May 2019

The first author was partially supported by Leverhulme Trust Research Project Grant 2014-112. The second author was supported by the grant PN-Ⅲ-P4-ID-PCE-2016-0778 of the Romanian Ministry of Research and Innovation CNCS-UEFISCDI, within PNCDI Ⅲ

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Abstract

In this paper we present two dual pairs that can be seen as the linear analogues of the following two dual pairs related to fluids: the EPDiff dual pair due to Holm and Marsden, and the ideal fluid dual pair due to Marsden and Weinstein.

Keywords:

Mathematics Subject Classification: Primary: 53D20, 53D17; Secondary: 22E60, 17B08.

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References

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