Combinatorial proof for a stability property of plethysm coefficients

Plethysm coefficients are important structural constants in the representation the- ory of the symmetric groups and general linear groups. Remarkably, some sequences of plethysm coefficients stabilize (they are ultimately constants). In this paper we give a new proof of such a stability property, pr...

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Detalles Bibliográficos
Autores: Colmenarejo Hernando, Laura, Briand, Emmanuel
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2014
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/87750
Acceso en línea:https://hdl.handle.net/11441/87750
https://doi.org/10.1016/j.endm.2014.08.007
Access Level:acceso abierto
Palabra clave:Combinatorial representation theory
Symmetric functions
Plethysm
Descripción
Sumario:Plethysm coefficients are important structural constants in the representation the- ory of the symmetric groups and general linear groups. Remarkably, some sequences of plethysm coefficients stabilize (they are ultimately constants). In this paper we give a new proof of such a stability property, proved by Brion with geometric representation theory techniques. Our new proof is purely combinatorial: we decompose plethysm coefficients as a alternating sum of terms counting integer points in poly- topes, and exhibit bijections between these sets of integer points.