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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Symmetric functions in noncommuting variables


Authors: Mercedes H. Rosas and Bruce E. Sagan
Journal: Trans. Amer. Math. Soc. 358 (2006), 215-232
MSC (2000): Primary 05E05; Secondary 05E10, 05A18
Published electronically: December 28, 2004
MathSciNet review: 2171230
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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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Additional Information

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

Bruce E. Sagan
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027
Email: sagan@math.msu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03623-2
PII: S 0002-9947(04)03623-2
Keywords: Noncommuting variables, partition lattice, Schur function, symmetric function
Received by editor(s): October 26, 2002
Received by editor(s) in revised form: January 30, 2004
Published electronically: December 28, 2004
Article copyright: © Copyright 2004 American Mathematical Society