arXiv 0712.22012007-12-13math.COmath.RA

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

Lenny Tevlin

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

英文摘要：

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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