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CONJUGATION COINVARIANTS OF QUANTUM MATRICES

Published online by Cambridge University Press:  24 March 2003

M. DOMOKOS  and
T. H. LENAGAN
M. DOMOKOS
Affiliation:
Rényi Institute of Mathematics, Hungarian Academy of Sciences, P.O. Box 127, 1364 Budapest, [email protected]
T. H. LENAGAN
Affiliation:
Department of Mathematics, University of Edinburgh, James Clerk Maxwell Building, King's Buildings, Mayfield Road, Edinburgh EH9 3JZ [email protected]
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Abstract

A quantum deformation of the classical conjugation action of ${\rm GL}(N,{\bb C})$ on the space of $N\times N$ matrices $M(N,{\bb C})$ is defined via a coaction of the quantum general linear group ${\cal O}({\rm GL}_q(N,{\bb C}))$ on the algebra of quantum matrices ${\cal O}(M_q(N,{\bb C}))$ . The coinvariants of this coaction are calculated. In particular, interesting commutative subalgebras of ${\cal O}(M_q(N,{\bb C}))$ generated by (weighted) sums of principal quantum minors are obtained. For general Hopf algebras, co-commutative elements are characterized as coinvariants with respect to a version of the adjoint coaction.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 35 , Issue 1 , January 2003 , pp. 117 - 127
Copyright
© The London Mathematical Society 2003

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Footnotes

First author partially supported by OTKA No. F 32325 and T 34530. Most of this research was done during a visit to Edinburgh with the support of the London Mathematical Society and during the first author's Marie Curie Individual Fellowship held in Edinburgh.