scholarly journals The essential dimension of the normalizer of a maximal torus in the projective linear group

2009 ◽  
Vol 3 (4) ◽  
pp. 467-487 ◽  
Author(s):  
Aurel Meyer ◽  
Zinovy Reichstein
Keyword(s):  
Linear Group ◽  
Maximal Torus ◽  
Essential Dimension ◽  
Projective Linear Group

Flag-Transitive 3- (v, k,3) Designs and PSL(2,q) Groups

2021 ◽  
Vol 28 (01) ◽  
pp. 33-38
Author(s):  
Shaojun Dai ◽  
Shangzhao Li
Keyword(s):  
Linear Group ◽  
Automorphism Groups ◽  
Two Dimensional ◽  
Text Design ◽  
Projective Linear Group

This article is a contribution to the study of the automorphism groups of 3-[Formula: see text] designs. Let [Formula: see text] be a non-trivial 3-[Formula: see text] design. If a two-dimensional projective linear group [Formula: see text] acts flag-transitively on [Formula: see text], then [Formula: see text] is a 3-[Formula: see text] or 3-[Formula: see text] design.

scholarly journals THE SYMMETRIC GROUP REPRESENTATION ON COHOMOLOGY OF THE REGULAR ELEMENTS OF A MAXIMAL TORUS OF THE SPECIAL LINEAR GROUP

2008 ◽  
Vol 84 (1) ◽  
pp. 85-98
Author(s):  
ANTHONY HENDERSON
Keyword(s):  
Symmetric Group ◽  
Linear Group ◽  
Maximal Torus ◽  
Group Representation ◽  
Special Linear Group ◽  
Special Linear ◽  
Regular Elements ◽  
Isotypic Component

AbstractWe give a formula for the character of the representation of the symmetric group Sn on each isotypic component of the cohomology of the set of regular elements of a maximal torus of SLn, with respect to the action of the centre.

scholarly journals Automorphisms of Drinfeld half-spaces over a finite field

2013 ◽  
Vol 149 (7) ◽  
pp. 1211-1224 ◽  
Author(s):  
Bertrand Rémy ◽  
Amaury Thuillier ◽  
Annette Werner
Keyword(s):  
Automorphism Group ◽  
Finite Field ◽  
Vector Space ◽  
Half Space ◽  
Linear Group ◽  
Analytic Geometry ◽  
Base Field ◽  
Projective Linear Group

AbstractWe show that the automorphism group of Drinfeld’s half-space over a finite field is the projective linear group of the underlying vector space. The proof of this result uses analytic geometry in the sense of Berkovich over the finite field equipped with the trivial valuation. We also take into account extensions of the base field.

scholarly journals On a rationality problem for fields of cross-ratios II

2020 ◽  
pp. 1-11
Author(s):  
Tran-Trung Nghiem ◽  
Zinovy Reichstein
Keyword(s):  
Symmetric Group ◽  
Linear Group ◽  
Fixed Field ◽  
Independent Variables ◽  
Odd Order ◽  
Projective Linear Group ◽  
Rationality Problem

Abstract Let k be a field, $x_1, \dots , x_n$ be independent variables and let $L_n = k(x_1, \dots , x_n)$ . The symmetric group $\operatorname {\Sigma }_n$ acts on $L_n$ by permuting the variables, and the projective linear group $\operatorname {PGL}_2$ acts by $$ \begin{align*} \begin{pmatrix} a & b \\ c & d \end{pmatrix}\, \colon x_i \longmapsto \frac{a x_i + b}{c x_i + d} \end{align*} $$ for each $i = 1, \dots , n$ . The fixed field $L_n^{\operatorname {PGL}_2}$ is called “the field of cross-ratios”. Given a subgroup $S \subset \operatorname {\Sigma }_n$ , H. Tsunogai asked whether $L_n^S$ rational over $K_n^S$ . When $n \geqslant 5,$ the second author has shown that $L_n^S$ is rational over $K_n^S$ if and only if S has an orbit of odd order in $\{ 1, \dots , n \}$ . In this paper, we answer Tsunogai’s question for $n \leqslant 4$ .

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