Symmetric Functions in Noncommuting Variables

    Mercedes H. Rosas (joint work with Bruce Sagan)

Departamento de Matematicas Universidad Simon Bolivar

Consider the algebra of formal power series in countable many noncommuting variables over the rationals. The subalgebra \Pi(x) of symmetric functions in noncommuting variables consists of all elements invariant under permutations of the variables and of bounded degree. We develop a theory of such functions analogous to the ordinary theory of symmetric functions. In particular, we define analogs of the monomial, power sum, elementary, and complete homogeneous, and Schur symmetric functions as well as investigating their properties.

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Slides for the talk