### Abstract

Original language | English |
---|---|

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 |

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**The geometric meaning of Zhelobenko operators.** / Sevastyanov, A. .

Research output: Contribution to journal › Article

*Transformation Groups*, vol. 18, no. 3, pp. 865-875. https://doi.org/10.1007/s00031-013-9234-9

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TY - JOUR

T1 - The geometric meaning of Zhelobenko operators

AU - Sevastyanov, A.

PY - 2013/9/1

Y1 - 2013/9/1

N2 - 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.

AB - 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.

U2 - 10.1007/s00031-013-9234-9

DO - 10.1007/s00031-013-9234-9

M3 - Article

VL - 18

SP - 865

EP - 875

JO - Transformation Groups

JF - Transformation Groups

SN - 1083-4362

IS - 3

ER -