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  1. Home > Articles & Issues >
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  3. Pieri rules for Schu ...
Conference paper

Pieri rules for Schur functions in superspace

Miles Eli Jones (1), Luc Lapointe (1)
(1) Instituto de Matemática y Física - Universidad de Talca
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Imported on
November 21, 2016
Published on
December 31, 2014
Last modified on
March 31, 2025
Volume
DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Proceedings
DOI
10.46298/dmtcs.2497
License
Attribution 4.0 International (CC BY 4.0)
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Pieri rules for Schur functions in superspace

Miles Eli Jones (1), Luc Lapointe (1)
(1) Instituto de Matemática y Física - Universidad de Talca
Abstract
English
The Schur functions in superspace $s_\Lambda$ and $\overline{s}_\Lambda$ are the limits $q=t= 0$ and $q=t=\infty$ respectively of the Macdonald polynomials in superspace. We present the elementary properties of the bases $s_\Lambda$ and $\overline{s}_\Lambda$ (which happen to be essentially dual) such as Pieri rules, dualities, monomial expansions, tableaux generating functions, and Cauchy identities.
French
Les fonctions de Schur dans le superespace $s_\Lambda$ et $\overline{s}_\Lambda$ sont les limites $q=t= 0$ et $q=t=\infty$ respectivement des polynômes de Macdonald dans le superespace. Nous présentons les propriétés élémentaires des bases $s_\Lambda$ et $\overline{s}_\Lambda$ (qui sont essentiellement duales l'une de l'autre) tels que les règles de Pieri, la dualité, le développement en fonctions monomiales, les fonctions génératrices de tableaux et les identités de Cauchy.
Keywords
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • Schur functions
  • Key polynomials
  • symmetric functions in superspace
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