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Schur-Weyl duality and the free Lie algebra


Authors: Stephen Doty and J. Matthew Douglass
Journal: Proc. Amer. Math. Soc. 145 (2017), 3263-3277
MSC (2010): Primary 17B01, 20G43
DOI: https://doi.org/10.1090/proc/13571
Published electronically: January 31, 2017
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Abstract: We prove an analogue of Schur-Weyl duality for the space of homogeneous Lie polynomials of degree $ r$ in $ n$ variables.


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Stephen Doty
Affiliation: Department of Mathematics and Statistics, Loyola University Chicago, Chicago, Illinois 60660
Email: doty@math.luc.edu

J. Matthew Douglass
Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203
Email: douglass@unt.edu

DOI: https://doi.org/10.1090/proc/13571
Keywords: Schur-Weyl duality, free Lie algebra
Received by editor(s): September 28, 2015
Received by editor(s) in revised form: September 7, 2016
Published electronically: January 31, 2017
Additional Notes: This work was partially supported by grants from the Simons Foundation (Grant #245975 to the first author and #245399 to the second author)
The second author would like to acknowledge that some of this material is based upon work supported by (while serving at) the National Science Foundation
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2017 American Mathematical Society