Unitriangular shape of decomposition matrices of unipotent blocks

Brunat, Olivier; Dudas, Olivier; Taylor, Jay

doi:10.4007/annals.2020.192.2.7

Cited by 16 publications

(19 citation statements)

References 55 publications

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“…8.1]. When s = 1, the set of unipotent characters forms a unitriangular basic set when both p and ℓ are good for G by recent work of Brunat, Dudas and Taylor [12], and then Assumption 5.3 is true for this case. For unipotent blocks of certain classical groups at the bad prime ℓ = 2, Chaneb [18] proved that there are also unitriangular basic sets; for example, Assumption 5.3 holds for all irreducible Brauer characters of symplectic groups at the prime 2, see [29,Cor.…”

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

confidence: 98%

“…In this way, Assumption 5.3 holds if the unitriangularity of the decomposition matrix is known. For example, we mention that the unipotent characters form unitriangular basic sets at good primes by recent work of Brunat, Dudas and Taylor [12].…”

Section: Introductionmentioning

confidence: 95%

“…For even q, the proof for odd q in [28] also applies, using the weights given in [43, §6]. For the case G = Spin + 8 (q), the assumption that ℓ is linear in [28] is to ensure a unitriangular basic set, which is known by [12] now.…”

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

confidence: 99%

See 2 more Smart Citations

Jordan decomposition for weights and the blockwise Alperin weight conjecture

Feng¹,

Li²,

Zhang³

2021

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

confidence: 98%

Section: Introductionmentioning

confidence: 95%

See 1 more Smart Citation

Jordan decomposition for weights and the blockwise Alperin weight conjecture

Feng¹,

Li²,

Zhang³

2021

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“…Ad is smooth with differential T (1,X) which is onto by equation 14. All the varieties in question are smooth and so there exists a Zariski open (and hence analytically open Analogous results to Lemma 2.6 and corollary 2.7 hold for nilpotent orbits of g, though different proof methods must be used (see [BDT20,Lemma 5.10] for details).…”

Section: We Now Show Thatmentioning

confidence: 97%

The wavefront set over a maximal unramified field extension

Okada¹

2021

Preprint

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We calculate the wavefront set of spherical Arthur representations of split p-adic reductive groups -the spherical representations expected to occur as local factors of automorphic representations. We do this by developing new finer invariants for irreducible admissible representations of p-adic groups and showing that for spherical Arthur representations they can be computed in terms of equivariant perverse sheaves on the nilpotent cone of the Langlands dual group.

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“…The McKay conjecture has been reduced to a so-called inductive McKay condition about quasi-simple groups by Isaacs-Malle-Navarro [IMN07] and the first requirement is an Out(X)-equivariant bijection realizing McKay's equality. Determining the action of Out(G) on Irr(G) for all quasi-simple groups G would also have applications to other conjectures about characters with similar reductions such as the Alperin-McKay conjecture or the Dade conjecture (see [S13], [S17]) or even conjectures about modular characters (see [NT11]) through the unitriangularity of decomposition matrices (see [BDT20]).…”

Section: Introductionmentioning

confidence: 99%

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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Unitriangular shape of decomposition matrices of unipotent blocks

Cited by 16 publications

References 55 publications

Jordan decomposition for weights and the blockwise Alperin weight conjecture

Jordan decomposition for weights and the blockwise Alperin weight conjecture

The wavefront set over a maximal unramified field extension

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

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