Symmetric Functions in Noncommuting Variables

Details Symmetric Functions in Noncommuting Variables Symmetric Functions in Noncommuting Variables

2002-08-22

arxiv.org/abs/math/0208168v2

Mathematics

Combinatorics

16 pages, Latex, see related papers at http://www.math.msu.edu/~sagan, to appear in Transactions of the American Mathematica

Scientific paper

Consider the algebra Q<> of formal power series in countably many noncommuting variables over the rationals. The subalgebra Pi(x_1,x_2,...) of symmetric functions in noncommuting variables consists of all elements invariant under permutation 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, complete homogeneous, and Schur symmetric functions as will as investigating their properties.

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