A canonical expansion of the product of two Stanley symmetric functions
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10801_2013_Article_469.pdf
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Author(s)
Li, Nan
Date Issued
September 2013
Journal
Journal of Algebraic Combinatorics
Publisher
Springer US
Citation
Li, Nan. “A Canonical Expansion of the Product of Two Stanley Symmetric Functions.” Journal of Algebraic Combinatorics 39.4 (2014): 833–851.
Version
Author's final manuscript
Abstract
We study the problem of expanding the product of two Stanley symmetric functions F[subscript w]⋅F[subscript u] into Stanley symmetric functions in some natural way. Our approach is to consider a Stanley symmetric function as a stabilized Schubert F[subscript w] = lim[subscript n →∞] S[subscript 1[superscipt n]x w], and study the behavior of the expansion of S[subscript 1[superscript n] x w]⋅S[subscript 1[superscript n] x u] into Schubert polynomials as n increases. We prove that this expansion stabilizes and thus we get a natural expansion for the product of two Stanley symmetric functions. In the case when one permutation is Grassmannian, we have a better understanding of this stability. We then study some other related stability properties, providing a second proof of the main result.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s10801-013-0469-2
