On the centralizer of a balanced nilpotent section

Hardesty, William

doi:10.48550/arxiv.1810.06157

Cited by 3 publications

(5 citation statements)

References 7 publications

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“…Proof. These claims are proved in [H2,Theorem 1.6,Theorem 1.8]. A different argument for smoothness is also given in §3.4 below.…”

Section: The Springer Resolutionmentioning

confidence: 93%

Integral exotic sheaves and the modular Lusztig-Vogan bijection

Achar,

Hardesty,

Riche

2018

Preprint

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Let G be a reductive group over an algebraically closed field k of very good characteristic. The Lusztig-Vogan bijection is a bijection between the set of dominant weights for G and the set of irreducible G-equivariant vector bundles on nilpotent orbits, conjectured by Lusztig and Vogan independently, and constructed in full generality by Bezrukavnikov. In characteristic 0, this bijection is related to the theory of 2-sided cells in the affine Weyl group, and plays a key role in the proof of the Humphreys conjecture on support varieties of tilting modules for quantum groups at a root of unity.In this paper, we prove that the Lusztig-Vogan bijection is (in a way made precise in the body of the paper) independent of the characteristic of k. This allows us to extend all of its known properties from the characteristic-0 setting to the general case. We also expect this result to be a step towards a proof of the Humphreys conjecture on support varieties of tilting modules for reductive groups in positive characteristic.

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“…Proof. These claims are proved in [H2,Theorem 1.6,Theorem 1.8]. A different argument for smoothness is also given in §3.4 below.…”

Section: The Springer Resolutionmentioning

confidence: 93%

Integral exotic sheaves and the modular Lusztig-Vogan bijection

Achar,

Hardesty,

Riche

2018

Preprint

Self Cite

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show abstract

“…Proof. These claims are proved in [25,Theorems 1.6 and 1.8]. A different argument for smoothness is also given in Section 3.4 below.…”

Section: Theorem 32 (Mcninch)mentioning

confidence: 94%

“…The second author has shown [25] that 𝑍 𝐺 (𝑥) is a smooth group scheme over 𝕆. In the companion paper [8], we study the representation theory of disconnected reductive groups, and we use this study here to establish the following result.…”

Section: Independence Of 𝕜: Representations Of Stabilizersmentioning

confidence: 99%

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Integral exotic sheaves and the modular Lusztig–Vogan bijection

Achar

Hardesty

Riche

2022

Journal of London Math Soc

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Let 𝐺 be a reductive algebraic group over an algebraically closed field 𝕜 of pretty good characteristic. The Lusztig-Vogan bijection is a bijection between the set of dominant weights for 𝐺 and the set of irreducible 𝐺-equivariant vector bundles on nilpotent orbits, conjectured by Lusztig and Vogan independently, and constructed in full generality by Bezrukavnikov. In characteristic 0, this bijection is related to the theory of 2-sided cells in the affine Weyl group, and plays a key role in the proof of the Humphreys conjecture on support varieties of tilting modules for quantum groups at a root of unity. In this paper, we prove that the Lusztig-Vogan bijection is (in a way made precise in the body of the paper) independent of the characteristic of 𝕜. This allows us to extend all of its known properties from the characteristic-0 setting to the general case. We also expect this result to be a step towards a proof of the Humphreys conjecture on support varieties of tilting modules for reductive groups in positive characteristic.

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“…This is equivalent to requiring G to be standard in the sense of [14, §4]. It follows from [8,Theorem 1.8] and [3,Lemma 2.1] that when p is pretty good for G, it does not divide the order of G x /(G x ) • ∼ = G x red /(G x red ) • for any nilpotent element x. As an immediate consequence of Theorem 1.1 and Lemma 2.2 below, we have the following result.…”

Section: Introductionmentioning

confidence: 99%