Supercharacter formulas for pattern groups

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 (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.

[1]  Discrete series and the unipotent subgroup , 1974 .

[2]  I. Reiner,et al.  ASSOCIATIVE ALGEBRAS(Graduate Texts in Mathematics, 88) , 1983 .

[3]  Roger W. Carter,et al.  Finite groups of Lie type: Conjugacy classes and complex characters , 1985 .

[4]  Meinolf Geck,et al.  Finite groups of Lie type , 1985 .

[5]  P. Diaconis,et al.  Comparison Techniques for Random Walk on Finite Groups , 1993 .

[6]  C. André.  Basic Characters of the Unitriangular Group , 1995 .

[7]  G. Robinson.  Counting conjugacy classes of unitriangular groups associated to finite-dimensional algebras , 1998 .

[8]  C. André.  Irreducible Characters of Finite Algebra Groups , 1998, math/9811132.

[9]  C. André.  The Basic Character Table of the Unitriangular Group , 2001 .

[10]  Ning Yan.  Representation theory of the finite unipotent linear groups , 2001 .

[11]  C. André.  Basic characters of the unitriangular group (for arbitrary primes) , 2002 .

[12]  P. Diaconis,et al.  A super-class walk on upper-triangular matrices , 2003 .

[13]  A. Vera-López,et al.  Computing in unitriangular matrices over finite fields , 2004 .

[14]  C. André,et al.  Super-characters of finite unipotent groups of types B n , C n and D n , 2006 .

[15]  I. Isaacs.  Counting characters of upper triangular groups , 2007 .

[16]  P. Diaconis,et al.  Supercharacters and superclasses for algebra groups , 2007 .

[17]  C. André,et al.  Supercharacters of the adjoint group of a finite radical ring , 2008 .