Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-24T22:57:30.006Z Has data issue: false hasContentIssue false
  • English
  • Français

Normality of orbit closures in the enhanced nilpotent cone

Published online by Cambridge University Press:  11 January 2016

Pramod N. Achar ,
Anthony Henderson  and
Benjamin F. Jones
Pramod N. Achar
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803, [email protected]
Anthony Henderson
Affiliation:
School of Mathematics and Statistics, University of Sydney, NSW 2006, [email protected]
Benjamin F. Jones
Affiliation:
Department of Mathematics, Statistics, and Computer Science, University of Wisconsin-Stout Menomonie, Wisconsin 54751, [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We continue the study of the closures of GL(V)-orbits in the enhanced nilpotent cone V × N begun by the first two authors. We prove that each closure is an invariant-theoretic quotient of a suitably defined enhanced quiver variety. We conjecture, and prove in special cases, that these enhanced quiver varieties are normal complete intersections, implying that the enhanced nilpotent orbit closures are also normal.

Keywords

17B0814L30
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 203 , September 2011 , pp. 1 - 45
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2011

References

[AH] Achar, P. N. and Henderson, A., Orbit closures in the enhanced nilpotent cone, Adv. Math. 219 (2008), 27–62.CrossRefGoogle Scholar
[B] Broer, A., Normal nilpotent varieties in F4, J. Algebra 207 (1998), 427–448.Google Scholar
[D] Donkin, S., The normality of closures of conjugacy classes of matrices, Invent. Math. 101 (1990), 717–736.Google Scholar
[FGT] Finkelberg, M., Ginzburg, V., and Travkin, R., Mirabolic affine Grassmannian and character sheaves, Selecta Math. (N.S.) 14 (2009), 607–628.CrossRefGoogle Scholar
[J] Johnson, C. P., Enhanced nilpotent representations of a cyclic quiver, preprint, arXiv:1004.3595v1 [math.RT]Google Scholar
[Ka1] Kato, S., An exotic Deligne-Langlands correspondence for symplectic groups, Duke Math. J. 148 (2009), 305–371.Google Scholar
[Ka2] Kato, S., Deformations of nilpotent cones and Springer correspondences, Amer. J. Math. 133 (2011), 519–553.Google Scholar
[Kr] Kraft, H., Closures of conjugacy classes in G2, J. Algebra 126 (1989), 454–465.Google Scholar
[KP1] Kraft, H. and Procesi, C., Closures of conjugacy classes of matrices are normal, Invent. Math. 53 (1979), 224–247.Google Scholar
[KP2] Kraft, H. and Procesi, C., On the geometry of conjugacy classes in classical groups, Comment. Math. Helv. 57 (1982), 539–602.Google Scholar
[M] Maffei, A., Quiver varieties of type A, Comment. Math. Helv. 80 (2005), 1–27.CrossRefGoogle Scholar
[S1] Sommers, E., Normality of nilpotent varieties in E6, J. Algebra 270 (2003), 288–306 CrossRefGoogle Scholar
[S2] Sommers, E., Normality of very even nilpotent varieties in D2l , Bull. Lond. Math. Soc. 37 (2005), 351–360.Google Scholar
[T] Travkin, R., Mirabolic Robinson-Shensted-Knuth correspondence, Selecta Math. (N.S.) 14 (2009), 727–758.Google Scholar