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

DOI:
https://doi.org/10.1090/S0002-9939-2010-10478-1

Published electronically:
July 13, 2010

MathSciNet review:
2729074

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Abstract: In contrast to the classical and semiclassical settings, the Coxeter element which cycles the columns of an 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 . 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 .

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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:
https://doi.org/10.1090/S0002-9939-2010-10478-1

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.