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

 

Supercharacter formulas for pattern groups


Authors: Persi Diaconis and Nathaniel Thiem
Journal: Trans. Amer. Math. Soc. 361 (2009), 3501-3533
MSC (2000): Primary 20C99, 05Exx
Published electronically: March 4, 2009
MathSciNet review: 2491890
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Abstract: C. Andre and N. Yan introduced the idea of a supercharacter theory to give a tractable substitute for character theory in wild groups such as the unipotent uppertriangular group $ U_n(\mathbb{F}_q)$. In this theory superclasses are certain unions of conjugacy classes, and supercharacters are a set of characters which are constant on superclasses. This paper gives a character formula for a supercharacter evaluated at a superclass for pattern groups and more generally for algebra groups.


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Additional Information

Persi Diaconis
Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305-4065

Nathaniel Thiem
Affiliation: Department of Mathematics, Stanford University, 450 Serra Mall, Building 380, Stanford, California 94305-2125
Address at time of publication: Department of Mathematics, University of Colorado, Campus Box 395, Boulder, Colorado 80309-0395

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04521-8
PII: S 0002-9947(09)04521-8
Keywords: Supercharacters, superclasses, finite unipotent group, algebra group, posets
Received by editor(s): October 5, 2006
Received by editor(s) in revised form: March 1, 2007
Published electronically: March 4, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.