On commuting varieties of upper triangular matrices

Basili, Roberta

doi:10.1080/00927872.2016.1178272

Cited by 3 publications

(1 citation statement)

References 5 publications

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“…and the stack: Stack n = Comm n /B where B ⊂ GL n denotes the Borel subgroup of lower triangular matrices. The variety Comm n has been studied in the literature, and we refer the reader to [3] for a survey, where the author proves that the dimension and number of irreducible components of Comm n grow wildly as n increases. However, we are interested only in the particular cases n ∈ {1, 2, 3, 4}, when this variety is behaved rather mildly: Proposition 5.9.…”

Section: Appendixmentioning

confidence: 99%

Hecke correspondences for smooth moduli spaces of sheaves

Neguţ¹

2018

Preprint

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We define functors on the derived category of the moduli space M of stable sheaves on a smooth projective surface (under Assumptions A and S below), and prove that these functors satisfy certain relations. These relations allow us to prove that the given functors induce an action of the elliptic Hall algebra on the K-theory of the moduli space M, thus generalizing the action studied by Nakajima, Grojnowski and Baranovsky in cohomology.

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Section: Appendixmentioning

confidence: 99%

Hecke correspondences for smooth moduli spaces of sheaves

Neguţ¹

2018

Preprint

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Hecke correspondences for smooth moduli spaces of sheaves

Neguţ

2022

Publ.math.IHES

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We define functors on the derived category of the moduli space ℳ of stable sheaves on a smooth projective surface (under Assumptions A and S below), and prove that these functors satisfy certain commutation relations. These relations allow us to prove that the given functors induce an action of the elliptic Hall algebra on the $K$ K -theory of the moduli space ℳ, thus generalizing the action studied by Nakajima, Grojnowski and Baranovsky in cohomology.

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On commuting varieties of parabolic subalgebras

Goddard

Goodwin

2018

Journal of Pure and Applied Algebra

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Let G be a connected reductive algebraic group over an algebraically closed field k, and assume that the characteristic of k is zero or a pretty good prime for G. Let P be a parabolic subgroup of G and let p be the Lie algebra of P . We consider the commuting varietyOur main theorem gives a necessary and sufficient condition for irreducibility of C(p) in terms of the modality of the adjoint action of P on the nilpotent variety of p. As a consequence, for the case P = B a Borel subgroup of G, we give a classification of when C(b) is irreducible; this builds on a partial classification given by Keeton. Further, in cases where C(p) is irreducible, we consider whether C(p) is a normal variety. In particular, this leads to a classification of when C(b) is normal.

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On commuting varieties of upper triangular matrices

Cited by 3 publications

References 5 publications

Hecke correspondences for smooth moduli spaces of sheaves

Hecke correspondences for smooth moduli spaces of sheaves

Hecke correspondences for smooth moduli spaces of sheaves

On commuting varieties of parabolic subalgebras

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