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

 

A categorification of integral Specht modules


Authors: Mikhail Khovanov, Volodymyr Mazorchuk and Catharina Stroppel
Journal: Proc. Amer. Math. Soc. 136 (2008), 1163-1169
MSC (2000): Primary 17B10, 05E10, 20C08
Published electronically: December 18, 2007
MathSciNet review: 2367090
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Abstract: We suggest a simple definition for categorification of modules over rings and illustrate it by categorifying integral Specht modules over the symmetric group and its Hecke algebra via the action of translation functors on some subcategories of category $ \mathcal{O}$ for the Lie algebra $ \mathfrak{sl}_n(\mathbb{C})$.


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Additional Information

Mikhail Khovanov
Affiliation: Department of Mathematics, Columbia University, New York, New York
Email: khovanov@math.columbia.edu

Volodymyr Mazorchuk
Affiliation: Department of Mathematics, Uppsala University, Uppsala, Sweden
Email: mazor@math.uu.se

Catharina Stroppel
Affiliation: Department of Mathematics, University of Glasgow, Glasgow, United Kingdom
Email: c.stroppel@maths.gla.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09124-1
PII: S 0002-9939(07)09124-1
Received by editor(s): September 14, 2006
Published electronically: December 18, 2007
Additional Notes: The first author was partially supported by the NSF grant DMS-0407784.
The second author was supported by STINT, the Royal Swedish Academy of Sciences, the Swedish Research Council and the MPI in Bonn.
The third author was supported by EPSRC grant 32199
Communicated by: Dan Barbasch
Article copyright: © Copyright 2007 American Mathematical Society