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Title:  KTheory Of Weight Varieties And Divided Difference Operators In Equivariant KkTheory 
Authors:  Leung, Ho Hon 
Keywords:  Symplectic Geometry Operator Algebras Divided difference operators KKtheory 
Issue Date:  31May2011 
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 simplyconnected 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. 
Committee Chair:  Sjamaar, Reyer 
Committee Member:  Holm, Tara S. Knutson, Allen 
Discipline:  Mathematics 
Degree Name:  Ph.D. of Mathematics 
Degree Level:  Doctor of Philosophy 
Degree Grantor:  Cornell University 
No Access Until:  20160929 
URI:  http://hdl.handle.net/1813/29318 
Appears in Collections:  Theses and Dissertations (CLOSED)

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