Transactions of the American Mathematical Society

Author(s): Mercedes H. Rosas; Bruce E. Sagan
Journal: Trans. Amer. Math. Soc. 358 (2006), 215-232.
MSC (2000): Primary 05E05; Secondary 05E10, 05A18
Posted: December 28, 2004
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Abstract: Consider the algebra $\mathbb{Q}\langle \langle x_1,x_2,\ldots\rangle \rangle$ of formal power series in countably many noncommuting variables over the rationals. The subalgebra $\Pi(x_1,x_2,\ldots)$ 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 well as investigating their properties.

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Mercedes H. Rosas
Affiliation: Departamento de Matemáticas, Universidad Simón Bolívar, Apdo. Postal 89000, Caracas, Venezuela
Address at time of publication: Department of Mathematics & Statistics, York University, Toronto, Ontario, Canada M3J 1P3
Email: mrosas@ma.usb.ve

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