Sign sequences and decomposition numbers
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- by Kai Meng Tan and Wei Hao Teo PDF
- Trans. Amer. Math. Soc. 365 (2013), 6385-6401 Request permission
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.References
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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
- MR Author ID: 656415
- 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
- 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.
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 365 (2013), 6385-6401
- MSC (2010): Primary 17B37, 20C08, 20C30, 20G43
- DOI: https://doi.org/10.1090/S0002-9947-2013-05860-6
- MathSciNet review: 3105756