Cônes nilpotents des super algèbres de Lie orthosymplectiques

Gruson, Caroline; Leidwanger, Séverine

doi:10.5802/ambp.285

Cited by 7 publications

(9 citation statements)

References 6 publications

(13 reference statements)

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“…A G 0 -equivariant resolution of the singularities of N 1 is constructed in [GrLe09]. Let us describe this resolution.…”

Section: Some Basic Facts About Odd Nilpotent Orbitsmentioning

confidence: 99%

“…Definition 1.1. (See [GrLe09].) The mixed Borel subalgebra containing b 0 is defined by the ordering: e 1 , f 1 , e 2 , f 2 , .…”

Section: Some Basic Facts About Odd Nilpotent Orbitsmentioning

confidence: 99%

“…Let osp(2n + 1, 2n) be the Lie superalgebra, called the orthosymplectic Lie superalgebra, consisting in endomorphisms of V which preserve the bilinear super-symmetric form and the graduation (for more details, see for example [GrLe09]). …”

Section: Some Basic Facts About Odd Nilpotent Orbitsmentioning

confidence: 99%

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Study of some orthosymplectic Springer fibers

Leidwanger

Perrin²

2011

Journal of Algebra

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“…A G 0 -equivariant resolution of the singularities of N 1 is constructed in [GrLe09]. Let us describe this resolution.…”

Section: Some Basic Facts About Odd Nilpotent Orbitsmentioning

confidence: 99%

“…Definition 1.1. (See [GrLe09].) The mixed Borel subalgebra containing b 0 is defined by the ordering: e 1 , f 1 , e 2 , f 2 , .…”

Section: Some Basic Facts About Odd Nilpotent Orbitsmentioning

confidence: 99%

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Study of some orthosymplectic Springer fibers

Leidwanger

Perrin²

2011

Journal of Algebra

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“…He also thanks the referee for careful reading and pointing out the errors in the original version. He owes the reference [9] to the referee. Partially supported by JSPS Grant-in-Aid for Scientific Research (B) #17340037.…”

Section: Acknowledgementsmentioning

confidence: 99%

“…There are many contributions to the resolutions of null fibers, among them we refer [12] and [19] for general theory; and [1,7,9,16,17,27] etc. for the present situation (or more general treatment).…”

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confidence: 99%

Resolution of null fiber and conormal bundles on the Lagrangian Grassmannian

Nishiyama

2009

Geom Dedicata

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We study the null fiber of a moment map related to dual pairs. We construct an equivariant resolution of singularities of the null fiber, and get conormal bundles of closed K C -orbits in the Lagrangian Grassmannian as categorical quotients. The conormal bundles thus obtained turn out to be a resolution of singularities of the closure of nilpotent K C -orbits, which is a "quotient" of the resolution of the null fiber. Mathematics Subject Classification (2000)Primary 14M15 · 14E15 · Secondary 14L30 · 22E47 · 20G05

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The nilpotent cone for classical Lie superalgebras

Jenkins

Nakano

2021

Proc. Amer. Math. Soc.

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In this paper the authors introduce an analogue of the nilpotent cone, N {\mathcal N} , for a classical Lie superalgebra, g {\mathfrak g} , that generalizes the definition for the nilpotent cone for semisimple Lie algebras. For a classical simple Lie superalgebra, g = g 0 ¯ ⊕ g 1 ¯ {\mathfrak g}={\mathfrak g}_{\bar 0}\oplus {\mathfrak g}_{\bar 1} with Lie G 0 ¯ = g 0 ¯ \text {Lie }G_{\bar 0}={\mathfrak g}_{\bar 0} , it is shown that there are finitely many G 0 ¯ G_{\bar 0} -orbits on N {\mathcal N} . Later the authors prove that the Duflo-Serganova commuting variety, X {\mathcal X} , is contained in N {\mathcal N} for any classical simple Lie superalgebra. Consequently, our finiteness result generalizes and extends the work of Duflo-Serganova on the commuting variety. Further applications are given at the end of the paper.

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Cônes nilpotents des super algèbres de Lie orthosymplectiques

Cited by 7 publications

References 6 publications

Study of some orthosymplectic Springer fibers

Study of some orthosymplectic Springer fibers

Resolution of null fiber and conormal bundles on the Lagrangian Grassmannian

The nilpotent cone for classical Lie superalgebras

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