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Special Transverse Slices and Their Enveloping Algebras

✍ Scribed by Alexander Premet

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
536 KB
Volume
170
Category
Article
ISSN
0001-8708

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✦ Synopsis

Let G be a simple, simply connected algebraic group over C; g ¼ Lie G; NðgÞ the nilpotent cone of g; and ðE; H; F Þ an sl 2 -triple in g: Let S ¼ E þ Ker ad F ; the special transverse slice to the adjoint orbit O of E; and S 0 ¼ S \ NðgÞ: The coordinate ring C½S 0 is naturally graded (See Slodowy, ''Simple Singularities and Simple Algebraic Groups,'' Lecture Notes in Mathematics, Vol. 815, Springer-Verlag, Berlin/ Heidelberg/New York, 1980). Let ZðgÞ be the centre of the enveloping algebra UðgÞ and Z : ZðgÞ ! C an algebra homomorphism. Identify g with g n via a Killing isomorphism and let w denote the linear function on g corresponding to E: Following Kawanaka (Generalized Gelfand-Graev representations and Ennola duality, in ''Algebraic Groups and Related Topics'' Advanced Studies in Pure

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