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

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

2007-12-13

arxiv.org/abs/0712.2201v1

Mathematics

Combinatorics

Based on the author's talk at FPSAC '07, Tianjin, China

Scientific paper

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.

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