scholarly journals DT-Invariants of Quivers and the Steinberg Character of GLn

2015 ◽  
Author(s):  
E. Letellier
Keyword(s):  
Steinberg Character

scholarly journals On the Steinberg Character of a Finite Simple Group of Lie Type

1971 ◽  
Vol 12 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Bhama Srinivasan
Keyword(s):  
Algebraic Group ◽  
Linear Algebraic Group ◽  
Simple Groups ◽  
Closed Field ◽  
Finite Simple Groups ◽  
Reductive Algebraic Group ◽  
Simple Algebraic Group ◽  
Simply Connected ◽  
Groups Of Lie Type ◽  
Steinberg Character

Let K be an algebraically closed field of characteristic ρ >0. If G is a connected, simple connected, semisimple linear algebraic group defined over K and σ an endomorphism of G onto G such that the subgroup Gσ of fixed points of σ is finite, Steinberg ([6] [7]) has shown that there is a complex irreducible character χ of Gσ with the following properties. χ vanishes at all elements of Gσ which are not semi- simple, and, if x ∈ G is semisimple, χ(x) = ±n(x) where n(x)is the order of a Sylow p-subgroup of (ZG(x))σ (ZG(x) is the centraliser of x in G). If G is simple he has, in [6], identified the possible groups Gσ they are the Chevalley groups and their twisted analogues over finite fields, that is, the ‘simply connected’ versions of finite simple groups of Lie type. In this paper we show, under certain restrictions on the type of the simple algebraic group G an on the characteristic of K, that χ can be expressed as a linear combination with integral coefficients of characters induced from linear characters of certain naturally defined subgroups of Gσ. This expression for χ gives an explanation for the occurence of n(x) in the formula for χ (x), and also gives an interpretation for the ± 1 occuring in the formula in terms of invariants of the reductive algebraic group ZG(x).

The Steinberg Character of Finite Classical Groups

2013 ◽  
Vol 20 (01) ◽  
pp. 163-168
Author(s):  
Xueling Song ◽  
Yanjun Liu
Keyword(s):  
Classical Group ◽  
Classical Groups ◽  
Characteristic P ◽  
Combinatorial Objects ◽  
Finite Classical Group ◽  
Finite Classical Groups ◽  
Steinberg Character

Let G be a finite classical group of characteristic p. In this paper, we give an arithmetic criterion of the primes r ≠ p, for which the Steinberg character lies in the principal r-block of G. The arithmetic criterion is obtained from some combinatorial objects (the so-called partition and symbol).

scholarly journals The Extended Steinberg Character

1995 ◽  
Vol 175 (1) ◽  
pp. 373-384 ◽  
Author(s):  
B. Muhlherr ◽  
P. Schmid
Keyword(s):  
Steinberg Character

scholarly journals On the Steinberg character of a semisimplep-adic group

2013 ◽  
Vol 265 (2) ◽  
pp. 499-509 ◽  
Author(s):  
Julee Kim ◽  
George Lusztig
Keyword(s):  
Steinberg Character
Sign in / Sign up

Export Citation Format

Share Document