### 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 |
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Pages (from-to) | 865-875 |

Number of pages | 11 |

Journal | Transformation Groups |

Volume | 18 |

Issue number | 3 |

Early online date | 16 Jul 2013 |

DOIs | |

Publication status | Published - 1 Sep 2013 |