The geometric meaning of Zhelobenko operators

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Let g be the complex semisimple Lie algebra associated to a complex semisimple algebraic group G, b a Borel subalgebra of g , h⊂b the Cartan sublagebra, and N ⊂ G the unipotent subgroup corresponding to the nilradical n⊂b . We show that the explicit formula for the extremal projection operator for g obtained by Asherova, Smirnov, and Tolstoy and similar formulas for Zhelobenko operators are related to the existence of a birational equivalence N×h→b given by the restriction of the adjoint action. Simple geometric proofs of formulas for the “classical” counterparts of the extremal projection operator and of Zhelobenko operators are also obtained.
Original languageEnglish
Pages (from-to)865-875
Number of pages11
JournalTransformation Groups
Issue number3
Early online date16 Jul 2013
Publication statusPublished - 1 Sept 2013


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