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Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras

Benedetti, Carolina
; 
Bergeron, Nantel
; 
Chen, Zhi
; 
Vinroot, C. Ryan
Abstract
We identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite field, and the ring of symmetric functions in noncommuting variables. Each is a Hopf algebra and the two are isomorphic as such. This allows developments in each to be transferred. The identification suggests a rich class of examples for the emerging field of combinatorial Hopf algebras. (C) 2012 Elsevier Inc. All rights reserved.
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2012-01-01
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Mathematics
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Mathematics
DOI
10.1016/j.aim.2011.12.024
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https://scholarworks.wm.edu/handle/internal/776
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