Descent equalities and the inductive McKay condition for types <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi mathvariant="sans-serif">B</mml:mi></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"><mml:mi mathvariant="sans-serif">E</mml:mi></mml:math>

Cabanes, Marc; Späth, Britta

doi:10.1016/j.aim.2019.106820

Cited by 18 publications

(17 citation statements)

References 26 publications

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“…In the investigation of the inductive condition of McKay conjecture (cf. [36, §10]), Cabanes and Späth proved in a series of papers [15][16][17]60] for ordinary characters that: in every G-orbit of Irr(G) there exists a character χ ∈ Irr(G) such that ( GA) χ = G χ A χ and χ extends to GA χ . Thus Assumption 5.3 holds if G has a ( GA)-stable unitriangular basic set for IBr(G, e G s ).…”

Section: Then Any Block B In S Is Baw-goodmentioning

confidence: 99%

Jordan decomposition for weights and the blockwise Alperin weight conjecture

Feng¹,

Li²,

Zhang³

2021

Preprint

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Section: Then Any Block B In S Is Baw-goodmentioning

confidence: 99%

Jordan decomposition for weights and the blockwise Alperin weight conjecture

Feng¹,

Li²,

Zhang³

2021

Preprint

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“…The aim of the present paper and its sequel [S21a] is to prove A(∞) for G of type D and 2 D. In the present paper G will be indeed some D l,sc (q) (l ≥ 4, q a power of an odd prime); the case of twisted types 2 D will also be deduced in [S21a]. Condition A(∞) in the case of D l,sc (2 m ) and 2 D l,sc (2 m ), essentially a corollary of [CS19,3.9], is also established in [S21a].…”

Section: Introductionmentioning

confidence: 92%

“…When G is the universal covering group of a finite simple group of Lie type, this is Question 5.9 in [GM]. Previous research on the subject has left open only the case of groups of type D, see [CS19,2.5]. The present paper is the first part of a solution to that problem.…”

Section: Introductionmentioning

confidence: 98%

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Extensions of characters in type D and the inductive McKay condition, I

Späth

2021

Preprint

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This is a contribution to the study of Irr(G) as an Aut(G)-set for G a finite quasi-simple group. Focusing on the last open case of groups of Lie type D and 2 D, a crucial property is the so-called condition A ′ (∞) expressing that diagonal automorphisms and graph-field automorphisms of G have transversal orbits in Irr(G). This is part of the stronger A(∞) condition introduced in the context of the reduction of the McKay conjecture to a question on quasi-simple groups. Our main theorem is that a minimal counter-example to condition A(∞) for groups of type D would still satisfy A ′ (∞). This will be used in a second paper to fully establish A(∞) for any type and rank. The present paper uses Harish-Chandra induction as a parametrization tool. We give a new, more effective proof of the theorem of Geck and Lusztig ensuring that cuspidal characters of arbitrary standard Levi subgroups of G = D l,sc (q) extend to their stabilizers in the normalizer of that Levi subgroup. This allows to control the action of automorphisms on these extensions. From there Harish Chandra theory leads naturally to a detailed study of associated relative Weyl groups and other extendibility problems in that context.

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“…Therefore, F 1 | G F generates B and then the claim holds. The required bijection Ξ B is indeed constructed in the proof of [CS19,Thm. 3.7].…”

Section: Simple Groups Of Lie Type In Non-defining Characteristicmentioning

confidence: 99%

Unitriangular basic sets, Brauer characters and coprime actions

Feng¹,

Späth²

2021

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We show that the unitriangularity of decomposition matrices is inherited by overgroups in the case of normal inclusions of finite groups with abelian quotient. Combining the theorem of Brunat-Dudas-Taylor for certain unipotent blocks and the equivalences of Bonnafé-Dat-Rouquier, this helps establishing the unitriangularity for many more blocks of quasi-simple groups of Lie type. This opens wider the door for applications to counting conjectures dealing with Brauer characters of finite groups and where reduction theorems require information about blocks of quasi-simple groups. We apply this to a conjecture of Navarro positing that Glauberman's theorem on coprime action also holds for Brauer characters. We reduce it to a problem on the unitriangular shape of the decomposition matrices of finite groups of Lie type in non-defining characteristic.

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Descent equalities and the inductive McKay condition for types B and E

Cited by 18 publications

References 26 publications

Jordan decomposition for weights and the blockwise Alperin weight conjecture

Jordan decomposition for weights and the blockwise Alperin weight conjecture

Extensions of characters in type D and the inductive McKay condition, I

Unitriangular basic sets, Brauer characters and coprime actions

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