Supercharacter formulas for pattern groups
Authors:
Persi Diaconis and Nathaniel Thiem
Journal:
Trans. Amer. Math. Soc. 361 (2009), 35013533
MSC (2000):
Primary 20C99, 05Exx
Published electronically:
March 4, 2009
MathSciNet review:
2491890
Fulltext PDF Free Access
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Additional Information
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 . 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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 André, C. ``Irreducible characters of finite algebra groups,'' Matrices and group representations Coimbra, 1998, Textos Mat. Sér B 19 (1999), 6580. MR 1773571 (2001g:20009)
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 André, C. ``Basic characters of the unitriangular group (for arbitrary primes),'' Proceedings of the American Mathematical Society 130 (2002), 19341954. MR 1896026 (2003g:20075)
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 André, C; Neto, A. ``Supercharacters of finite unipotent groups of types , and ,'' J. Algebra 305 (2006), 394429. MR 2264135 (2007j:20013)
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 André, C; Nicolás, A. ``Supercharacters of the adjoint group of a finite radical ring,'' August 2006 preprint.
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 Arregi, J; VeraLopez, A. ``Computing in unitriangular matrices over finite fields.'' Linear algebra applications 387 (2004), 193219. MR 2069276 (2005c:20082)
 8.
 AriasCastro, E; Diaconis, P; Stanley, R. ``A superclass walk on uppertriangular matrices,'' Journal of Algebra 278 (2004), 739765. MR 2071663 (2005f:60101)
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 Carter, R. Finite groups of Lie type: Conjugacy classes and complex characters. John Wiley and Sons, 1985. MR 794307 (87d:20060)
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 Yan, N. ``Representations of finite unipotent linear groups by the method of clusters,'' 2006 preprint.
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Additional Information
Persi Diaconis
Affiliation:
Department of Mathematics, Stanford University, Stanford, California 943054065
Nathaniel Thiem
Affiliation:
Department of Mathematics, Stanford University, 450 Serra Mall, Building 380, Stanford, California 943052125
Address at time of publication:
Department of Mathematics, University of Colorado, Campus Box 395, Boulder, Colorado 803090395
DOI:
http://dx.doi.org/10.1090/S0002994709045218
PII:
S 00029947(09)045218
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.
