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Supercharacters and superclasses for algebra groups
Author(s):
Persi
Diaconis;
I.
M.
Isaacs
Journal:
Trans. Amer. Math. Soc.
360
(2008),
2359-2392.
MSC (2000):
Primary 20C15, 20D15
Posted:
November 20, 2007
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Abstract:
We study certain sums of irreducible characters and compatible unions of conjugacy classes in finite algebra groups. These groups generalize the unimodular upper triangular groups over a finite field, and the supercharacter theory we develop extends results of Carlos André and Ning Yan that were originally proved in the upper triangular case. This theory sometimes allows explicit computations in situations where it would be impractical to work with the full character table. We discuss connections with the Kirillov orbit method and with Gelfand pairs, and we give conditions for a supercharacter or a superclass to be an ordinary irreducible character or conjugacy class, respectively. We also show that products of supercharacters are positive integer combinations of supercharacters.
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Additional Information:
Persi
Diaconis
Affiliation:
Department of Mathematics, Stanford University, 450 Serra Mall Bldg. 380, Stanford, California 94305
Email:
diaconis@math.stanford.edu
I.
M.
Isaacs
Affiliation:
Department of Mathematics, University of Wisconsin, 480 Lincoln Dr., Madison, Wisconsin 53706
Email:
isaacs@math.wisc.edu
DOI:
10.1090/S0002-9947-07-04365-6
PII:
S 0002-9947(07)04365-6
Received by editor(s):
December 30, 2005
Posted:
November 20, 2007
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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