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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Twisting the quantum grassmannian


Authors: S. Launois and T. H. Lenagan
Journal: Proc. Amer. Math. Soc. 139 (2011), 99-110
MSC (2010): Primary 16T20, 16P40, 16S38, 17B37, 20G42
Published electronically: July 13, 2010
MathSciNet review: 2729074
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Abstract: In contrast to the classical and semiclassical settings, the Coxeter element $ (12\dots n)$ which cycles the columns of an $ m\times n$ matrix does not determine an automorphism of the quantum grassmannian. Here, we show that this cycling can be obtained by means of a cocycle twist. A consequence is that the torus invariant prime ideals of the quantum grassmannian are permuted by the action of the Coxeter element $ (12\dots n)$. We view this as a quantum analogue of the recent result of Knutson, Lam and Speyer, where the Lusztig strata of the classical grassmannian are permuted by $ (12\dots n)$.


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Additional Information

S. Launois
Affiliation: School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, Kent CT2 7NF, United Kingdom
Email: S.Launois@kent.ac.uk

T. H. Lenagan
Affiliation: Maxwell Institute for Mathematical Sciences, School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, King’s Buildings, Mayfield Road, Edinburgh EH9 3JZ, United Kingdom
Email: tom@maths.ed.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10478-1
PII: S 0002-9939(2010)10478-1
Keywords: Quantum matrices, quantum grassmannian, cocycle twist, noncommutative dehomogenisation
Received by editor(s): October 1, 2009
Received by editor(s) in revised form: March 15, 2010
Published electronically: July 13, 2010
Additional Notes: The research of the first author was supported by a Marie Curie European Reintegration Grant within the $7^{th}$ European Community Framework Programme.
Communicated by: Martin Lorenz
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.