Noncommutative Analogs of Monomial Symmetric Functions, Cauchy Identity, and Hall Scalar Product

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This paper introduces noncommutative analogs of monomial symmetric functions and fundamental noncommutative symmetric functions. The expansion of ribbon Schur functions in both of these basis is nonnegative. With these functions at hand, one can derive a noncommutative Cauchy identity as well as study a noncommutative scalar product implied by Cauchy identity. This scalar product seems be the noncommutative analog of Hall scalar product in the commutative theory.
Based on the author's talk at FPSAC '07, Tianjin, China

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Combinatorics, Rings and Algebras, 05E05, 05A19

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http://salesiana.dossiersoluciones.com/handle/123456789/144166

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0712.2201
 http://arxiv.org/abs/0712.2201

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arXiv