# K-Theory Of Weight Varieties And Divided Difference Operators In Equivariant Kk-Theory

dc.contributor.author | Leung, Ho Hon | en_US |

dc.contributor.chair | Sjamaar, Reyer | en_US |

dc.contributor.committeeMember | Holm, Tara S. | en_US |

dc.contributor.committeeMember | Knutson, Allen | en_US |

dc.date.accessioned | 2012-06-28T20:57:02Z | |

dc.date.available | 2016-09-29T05:36:53Z | |

dc.date.issued | 2011-05-31 | en_US |

dc.description.abstract | This thesis consists of two chapters. In the first chapter, we compute the K theory of weight varieties by using techniques in Hamiltonian geometry. In the second chapter, we construct a set of divided difference operators in equivariant KK -theory. Let T be a compact torus and (M, [omega] ) a Hamiltonian T -space. In Chapter 1, we give a new proof of the K -theoretic analogue of the Kirwan surjectivity theorem in symplectic geometry (see [HL1]) by using the equivariant version of the Kirwan map introduced in [G2]. We compute the kernel of this equivariant Kirwan map. As an application, we find the presentation of the K -theory of weight varieties, which are the symplectic quotients of complete flag varieties G/T , as the quotient ring of the T -equivariant K -theory of flag varieties by the kernel of the Kirwan map, where G is a compact, connected and simply-connected Lie group. Demazure [D1], [D2], [D3] defined a set of isobaric divided difference operators on the representation ring R(T ). It can be seen as a decomposition of the classical Weyl character formula. In [HLS], Harada, Landweber and Sjamaar defined an analogous set of divided difference operators on the equivariant K -theory. In Chapter 2, we explicitly define these operators in the setting of equivariant KK theory first defined by Kasparov [K1], [K2]. It is a generalization of the results in [D3] and [HLS]. Due to the elegance and generality of equivariant KK -theory, some interesting applications of the result will also be given. | en_US |

dc.identifier.other | bibid: 7745175 | |

dc.identifier.uri | https://hdl.handle.net/1813/29318 | |

dc.language.iso | en_US | en_US |

dc.subject | Symplectic Geometry | en_US |

dc.subject | Operator Algebras | en_US |

dc.subject | Divided difference operators | en_US |

dc.subject | KK-theory | en_US |

dc.title | K-Theory Of Weight Varieties And Divided Difference Operators In Equivariant Kk-Theory | en_US |

dc.type | dissertation or thesis | en_US |

thesis.degree.discipline | Mathematics | |

thesis.degree.grantor | Cornell University | en_US |

thesis.degree.level | Doctor of Philosophy | |

thesis.degree.name | Ph. D., Mathematics |

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