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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Sign sequences and decomposition numbers


Authors: Kai Meng Tan and Wei Hao Teo
Journal: Trans. Amer. Math. Soc. 365 (2013), 6385-6401
MSC (2010): Primary 17B37, 20C08, 20C30, 20G43
Published electronically: August 19, 2013
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Abstract | References | Similar Articles | Additional Information

Abstract: We obtain a closed formula for the $ v$-decomposition numbers
$ d_{\lambda \mu }(v)$ arising from the canonical basis of the Fock space representation of $ U_v(\widehat {\mathfrak{sl}}_e)$, where the partition $ \lambda $ is obtained from $ \mu $ by moving some nodes in its Young diagram, all of which have the same $ e$-residue. We also show that when these $ v$-decomposition numbers are evaluated at $ v=1$, we obtain the corresponding decomposition numbers for the Schur algebras and symmetric groups.


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Additional Information

Kai Meng Tan
Affiliation: Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, Singapore 119076
Email: tankm@nus.edu.sg

Wei Hao Teo
Affiliation: Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, Singapore 119076
Email: tweihao@dso.org.sg

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05860-6
PII: S 0002-9947(2013)05860-6
Received by editor(s): January 27, 2012
Received by editor(s) in revised form: April 11, 2012
Published electronically: August 19, 2013
Additional Notes: This research was supported by MOE Academic Research Fund R-146-000-135-112. The authors thank Joseph Chuang for many helpful discussions resulting in this article.
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.