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

 

A new Littlewood-Richardson rule for Schur $ P$-functions


Author: Soojin Cho
Journal: Trans. Amer. Math. Soc. 365 (2013), 939-972
MSC (2010): Primary 05E05; Secondary 05E10
Published electronically: September 13, 2012
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Abstract: A new description of shifted Littlewood-Richardson coefficients is given in terms of semistandard decomposition tableaux which were recently introduced by L. Serrano. We also show that the set of semistandard decomposition tableaux is invariant under the action of Lascoux-Schützenberger involution, providing a combinatorial proof of the symmetry of Schur $ P$-functions. We find counterexamples to the conjecture made by L. Serrano on skew Schur $ P$-functions, proving the falsity of the conjecture. Many combinatorial properties of semistandard decomposition tableaux are also shown.


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Additional Information

Soojin Cho
Affiliation: Department of Mathematics, Ajou University, Suwon 443-749, Korea
Email: chosj@ajou.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05653-4
PII: S 0002-9947(2012)05653-4
Keywords: Schur $P$-functions, shifted tableaux, semistandard decomposition tableaux, shifted Littlewood-Richardson coefficients
Received by editor(s): March 29, 2011
Received by editor(s) in revised form: June 13, 2011
Published electronically: September 13, 2012
Additional Notes: This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0012398)
This work was done while the author was visiting the Korea Institute for Advanced Study.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.