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The down operator and expansions of near rectangular k-Schur functions
- Source :
- Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings vol. AR,..., Iss Proceedings (2012)
- Publication Year :
- 2012
- Publisher :
- Discrete Mathematics & Theoretical Computer Science, 2012.
-
Abstract
- We prove that the Lam-Shimozono ``down operator'' on the affine Weyl group induces a derivation of the affine Fomin-Stanley subalgebra of the affine nilCoxeter algebra. We use this to verify a conjecture of Berg, Bergeron, Pon and Zabrocki describing the expansion of k-Schur functions of ``near rectangles'' in the affine nilCoxeter algebra. Consequently, we obtain a combinatorial interpretation of the corresponding k-Littlewood–Richardson coefficients.
Details
- Language :
- English
- ISSN :
- 13658050
- Volume :
- DMTCS Proceedings vol. AR,...
- Issue :
- Proceedings
- Database :
- Directory of Open Access Journals
- Journal :
- Discrete Mathematics & Theoretical Computer Science
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.0f13ebbf3ec2430aa9da72a37c9a1e26
- Document Type :
- article
- Full Text :
- https://doi.org/10.46298/dmtcs.3052