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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Symmetric functions in noncommuting variables
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by Mercedes H. Rosas and Bruce E. Sagan PDF
Trans. Amer. Math. Soc. 358 (2006), 215-232 Request permission

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.
References
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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
  • MR Author ID: 152890
  • Email: sagan@math.msu.edu
  • Received by editor(s): October 26, 2002
  • Received by editor(s) in revised form: January 30, 2004
  • Published electronically: December 28, 2004
  • © Copyright 2004 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 358 (2006), 215-232
  • MSC (2000): Primary 05E05; Secondary 05E10, 05A18
  • DOI: https://doi.org/10.1090/S0002-9947-04-03623-2
  • MathSciNet review: 2171230