On the Sn-module structure of the noncommutative harmonics

Using the a noncommutative version of Chevalley’s theorem due to Bergeron, Reutenauer, Rosas, and Zabrocki we compute the graded Frobenius series for their two sets of noncommutative harmonics with respect to the left action of the symmetric group (acting on variables). We use these results to deriv...

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Detalles Bibliográficos
Autores: Briand, Emmanuel, Rosas Celis, Mercedes Helena, Zabrocki, Mike
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2008
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/41690
Acceso en línea:http://hdl.handle.net/11441/41690
https://doi.org/10.1016/j.jcta.2007.10.005
Access Level:acceso abierto
Palabra clave:proper multilinear polynomials
free Lie algebra
harmonics
coinvariants
symmetric functions
noncommutative polynomials
tensor algebra
Descripción
Sumario:Using the a noncommutative version of Chevalley’s theorem due to Bergeron, Reutenauer, Rosas, and Zabrocki we compute the graded Frobenius series for their two sets of noncommutative harmonics with respect to the left action of the symmetric group (acting on variables). We use these results to derive the Frobenius series for the enveloping algebra of the derived free Lie algebra in n variables.