## Advances in GeometryJean-Luc Brylinski, Ranee Brylinski, Victor Nistor, Boris Tsygan, Ping Xu This collection of invited mathematical papers by an impressive list of distinguished mathematicians is an outgrowth of the scientific activities at the Center for Geometry and Mathematical Physics of Penn State University. The articles present new results or discuss interesting perspectives on recent work that will be of interest to researchers and graduate students working in symplectic geometry and geometric quantization, deformation quantization, non-commutative geometry and index theory, quantum groups, holomorphic algebraic geometry and moduli spaces, quantum cohomology, algebraic groups and invariant theory, and characteristic classes. |

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### Contents

On Karabegovs Quantizations of Semisimple Coadjoint Orbits | 1 |

Exotic Differential Operators on Complex Minimal Nilpotent Orbits | 19 |

The Geometry Surrounding the ArnoldLiouville Theorem | 53 |

Copyright | |

13 other sections not shown

### Other editions - View all

Advances in Geometry, Volume 1 Jean-Luc Brylinski,Ranee Brylinski,Victor Nistor Limited preview - 2012 |

Advances in Geometry, Volume 1 Jean-Luc Brylinski,Ranee Brylinski,Victor Nistor No preview available - 2012 |

Advances in Geometry, Volume 1 Jean-Luc Brylinski,Ranee Brylinski,Victor Nistor No preview available - 1998 |

### Common terms and phrases

action acts arrangement associated associative algebra C*-algebras called canonical characters classes classical closed cohomology commutative compact complex condition Conjecture connection consider construct contains corresponding defined Definition deformation Deligne denote differential operators dimension element equal equation equivalence exact example exists extends fact fixed formula functions geometry gerbe given gives graded hamiltonian Hence hermitian holomorphic holonomy Idc(T identity implies induces integrable invariant isomorphism Lemma Lie algebra line bundle linkage manifold Math Mathematics metric moduli space morphism multiplication natural Note object obtain orbit particular polynomial principal projective Proof properties Proposition prove quantization quantum realization relations Remark representation respect restriction result ring satisfies Schubert sequence singular smooth space structure Suppose symbol symmetric symplectic Theorem theory unique University vector bundle vector fields vertices