# The geometric meaning of Zhelobenko operators

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1 Citation (Scopus)

### Abstract

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 language English 865-875 11 Transformation Groups 18 3 16 Jul 2013 https://doi.org/10.1007/s00031-013-9234-9 Published - 1 Sep 2013

### Fingerprint

Projection Operator
Geometric proof
Semisimple Lie Algebra
Semisimple Groups
Algebraic Groups
Operator
Subalgebra
Explicit Formula
Equivalence
Subgroup
Restriction
Meaning

### Cite this

In: Transformation Groups, Vol. 18, No. 3, 01.09.2013, p. 865-875.

Research output: Contribution to journalArticle

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