Results 11 - 20
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49
Geometric quantization on Kähler and symplectic manifolds
- International Congress of Mathematicians
, 2010
"... We explain various results on the asymptotic expansion of the Bergman ker-nel on Kähler manifolds and also on symplectic manifolds. We also review the “quantization commutes with reduction ” phenomenon for a compact Lie group action, and its relation to the Bergman kernel. ..."
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Cited by 10 (5 self)
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We explain various results on the asymptotic expansion of the Bergman ker-nel on Kähler manifolds and also on symplectic manifolds. We also review the “quantization commutes with reduction ” phenomenon for a compact Lie group action, and its relation to the Bergman kernel.
Geometric approaches to computing Kostka numbers and Littlewood-Richardson coefficients
- PH.D. DEGREE IN MATHEMATICS, MASSACHUSETTS INSTITUTE OF TECHNOLOGY (MIT
, 2004
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A symplectic proof of Verlinde factorization
- J. Diff. Geom
"... Abstract. We prove a multiplicity formula for Riemann-Roch numbers of reductions of Hamiltonian actions of loop groups. This includes as a special case the factorization formula for the quantum dimension of the moduli space of flat connections over a Riemann surface. Contents ..."
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Cited by 7 (5 self)
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Abstract. We prove a multiplicity formula for Riemann-Roch numbers of reductions of Hamiltonian actions of loop groups. This includes as a special case the factorization formula for the quantum dimension of the moduli space of flat connections over a Riemann surface. Contents
On the instanton complex of holomorphic Morse theory
, 2003
"... Consider a holomorphic torus action on a complex manifold which lifts to a holomorphic vector bundle. When the connected components of the fixed-point set form a partially ordered set, we construct, using sheaf-theoretical techniques, two spectral sequences that converges to the twisted Dolbeault co ..."
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Cited by 6 (2 self)
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Consider a holomorphic torus action on a complex manifold which lifts to a holomorphic vector bundle. When the connected components of the fixed-point set form a partially ordered set, we construct, using sheaf-theoretical techniques, two spectral sequences that converges to the twisted Dolbeault cohomology groups and those with compact support, respectively. These spectral sequences are the holomorphic counterparts of the instanton complex in standard Morse theory. The results proved imply holomorphic Morse inequalities and fixed-point formulas on a possibly non-compact manifold. Finally, examples and applications are given.
Holomorphic Morse inequalities in singular reduction
- Math. Res. Letters
, 1998
"... Abstract. We extend our Morse type inequalities for holomorphic symplectic reductions [TZ1, 2] to the case of singular reductions. 0. Introduction and the statement of main results Let (M, ω) be a closed symplectic manifold. We make the assumption that there is a Hermitian line bundle L over M admit ..."
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Cited by 6 (3 self)
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Abstract. We extend our Morse type inequalities for holomorphic symplectic reductions [TZ1, 2] to the case of singular reductions. 0. Introduction and the statement of main results Let (M, ω) be a closed symplectic manifold. We make the assumption that there is a Hermitian line bundle L over M admitting a Hermitian connection ∇L with the property that √−1
Quantum surfaces, special functions, and the tunneling effect
, 2001
"... The notion of quantum embedding is considered for two classes of examples: quantum coadjoint orbits in Lie coalgebras and quantum symplectic leaves in spaces with non-Lie permutation relations. A method for constructing irreducible representations of associative algebras and the corresponding trace ..."
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Cited by 4 (3 self)
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The notion of quantum embedding is considered for two classes of examples: quantum coadjoint orbits in Lie coalgebras and quantum symplectic leaves in spaces with non-Lie permutation relations. A method for constructing irreducible representations of associative algebras and the corresponding trace formulas over leaves with complex polarization are obtained. The noncommutative product on the leaves incorporates a closed 2-form and a measure which (in general) are different from the classical symplectic form and the Liouville measure. The quantum objects are related to some generalized special functions. The difference between classical and quantum geometrical structures could even occur to be exponentially small with respect to the deformation parameter. That is interpreted as a tunneling effect in the quantum geometry. Dedicated to the memory of Professor M. Flato 1
Spin c-Quantization and the K-multiplicities of the discrete series
, 2002
"... We express the K-multiplicities of a representation of the discrete series associated to a coadjoint orbit O in terms of Spin c-index on symplectic reductions of O. ..."
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Cited by 4 (2 self)
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We express the K-multiplicities of a representation of the discrete series associated to a coadjoint orbit O in terms of Spin c-index on symplectic reductions of O.
SYMPLECTIC REDUCTION AND A WEIGHTED MULTIPLICITY FORMULA FOR TWISTED SPIN C-DIRAC OPERATORS
, 1999
"... We extend our earlier work in [TZ1], where an analytic approach to the Guillemin-Sternberg conjecture [GS] was developed, to cases where the Spin c-complex under consideration is allowed to be further twisted by certain exterior power bundles of the cotangent bundle. The main result is a weighted qu ..."
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Cited by 3 (3 self)
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We extend our earlier work in [TZ1], where an analytic approach to the Guillemin-Sternberg conjecture [GS] was developed, to cases where the Spin c-complex under consideration is allowed to be further twisted by certain exterior power bundles of the cotangent bundle. The main result is a weighted quantization formula in the presence of commuting Hamiltonian actions. The corresponding Morse-type inequalities in holomorphic situations are also established.
Formal geometric quantization II
, 2009
"... In this paper we pursue the study of formal geometric quantization of non-compact Hamiltonian manifolds. Our main result is the proof that two quantization process coincide. This fact was obtained by Ma and Zhang in the preprint Arxiv:0812.3989 by completely different means. ..."
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Cited by 3 (0 self)
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In this paper we pursue the study of formal geometric quantization of non-compact Hamiltonian manifolds. Our main result is the proof that two quantization process coincide. This fact was obtained by Ma and Zhang in the preprint Arxiv:0812.3989 by completely different means.
