Algebraic Group Analogues of the Slodowy Slices and Deformations of Poisson W-algebras

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Abstract

We define algebraic group analogues of the Slodowy transversal slices to adjoint orbits in a complex semisimple Lie algebra Graphic. The new slices are transversal to the conjugacy classes in an algebraic group G with Lie algebra g. These slices are associated to (the conjugacy classes of) elements s of the Weyl group W of g. For such slices, we prove an analogue of the Kostant cross-section theorem for the action of a unipotent group. Using this theorem, we equip the new slices with certain Poisson structures obtained by Poisson reduction from a Poisson–Lie group structure on G.
Original languageEnglish
Pages (from-to)1880-1925
Number of pages46
JournalInternational Mathematics Research Notices
Volume2011
Issue number8
Early online date19 Jul 2010
DOIs
Publication statusPublished - 2011

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W-algebras
Algebraic Groups
Slice
Siméon Denis Poisson
Analogue
Conjugacy class
Semisimple Lie Algebra
Poisson Structure
Weyl Group
Theorem
Lie Algebra
Cross section
Orbit

Cite this

Algebraic Group Analogues of the Slodowy Slices and Deformations of Poisson W-algebras. / Sevastyanov, Alexey.

In: International Mathematics Research Notices, Vol. 2011, No. 8, 2011, p. 1880-1925.

Research output: Contribution to journalArticle

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