Browsing by Author "Chuah, MK"

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Dolbeault cohomology of G/(P,P)
(1999-03-01)
Chuah, MK
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Teo, LP
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應用數學系
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Department of Applied Mathematics
Let G be a complex connected semi-simple Lie group, with parabolic subgroup P. Let (P, P) be its commutator subgroup. The generalized Borel-Weil theorem on flag manifolds has an analogous result on the Dolbeault cohomology H-0,H-q(G/(P, P)). Consequently, the dimension of H-0,H-q(G/(P, P)) is either 0 or infinity. In this paper, we show that the Dolbeault operator <(partial derivative)over bar> has closed image, and apply the Peter-Weyl theorem to show how q determines the value 0 or infinity. For the case when P is maximal, we apply our result to compute the Dolbeault cohomology of certain examples, such as the punctured determinant bundle over the Grassmannian.
Equivalence classes of Vogan diagrams
(2004-09-01)
Chuah, MK
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Hu, CC
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應用數學系
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Department of Applied Mathematics
A Vogan diagram is a Dynkin diagram with an involution, and the vertices fixed by the involution may be painted. They represent real simple Lie algebras, and two diagrams are said to be equivalent if they represent the same Lie algebra. In this article we classify the equivalence classes of all Vogan diagrams. In doing so, we find that the underlying Dynkin diagrams have certain properties in graph painting. We show that this combinatorial property provides an easy classification for most of the simply-laced Dynkin diagrams. (C) 2004 Published by Elsevier Inc.
Extended Vogan diagrams
(2006-07-01)
Chuah, MK
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Hu, CC
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應用數學系
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Department of Applied Mathematics
An extended Vogan diagram is an extended Dynkin diagram with a diagram involution, such that the vertices fixed by the involution can be painted or unpainted. Every extended Vogan diagram represents an almost compact real form of some affine Kac-Moody Lie algebra. Two diagrams may represent isomorphic algebras, and in this case we say that the diagrams are equivalent. In this paper, we classify the equivalence classes of extended Vogan diagrams, and provide a complete list of all diagrams within each class. It gives a combinatorial classification of the isomorphic classes of almost compact real forms of the affine Kac-Moody Lie algebras. (c) 2006 Elsevier Inc. All rights reserved.
Holomorphic discrete models of semisimple Lie groups and their symplectic constructions
(2000-08-01)
Chuah, MK
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應用數學系
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Department of Applied Mathematics
Let G be a connected real semisimple Lie group which contains a compact Cartan subgroup such that it has non-empty discrete series. A holomorphic discrete model of G is a unitary G-representation consisting of all its holomorphic discrete series with multiplicity one. We perform geometric quantization to a class of G-invariant pseudo-Kahler manifolds and construct a holomorphic discrete model. The construction of discrete series which are not holomorphic is also discussed. (C) 2000 Academic Press.
Holomorphic sections of pre-quantum line bundles on G/(P, P)
(2000)
Chuah, MK
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應用數學系
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Department of Applied Mathematics
Let G = KAN be the Iwasawa decomposition of a complex connected semi-simple Lie group G. Let P subset of G be a parabolic subgroup containing AN, and let(P, P) be its commutator subgroup. In this paper, we characterize the K-invariant Kahler structures on G/(P, P), and study the holomorphic sections of their corresponding pre-quantum line bundles.
Holomorphic sections of prequantum line bundles on G/N
(1998-01-01)
Chuah, MK
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應用數學系
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Department of Applied Mathematics
Holomorphic sections of prequantum line bundles on G/N
(1998-01-01)
Chuah, MK
;
應用數學系
;
Department of Applied Mathematics
K-invariant Kaehler structures on K-C/N and the associated line bundles
(1996-11-01)
Chuah, MK
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交大名義發表
;
應用數學系
;
National Chiao Tung University
;
Department of Applied Mathematics
Let K be a compact semi-simple Lie group, and let N be a maximal unipotent subgroup of the complexified group Kc. classify ail the K-invariant Kaehler structures on K-C/N. structure w, let L be the line bundle with connection whose curvature is w. We then study the holomorphic sections of L, which constitute a K-representation space.
K-invariant Kaehler structures on K-C/N and the associated line bundles
(1996-11-01)
Chuah, MK
;
應用數學系
;
Department of Applied Mathematics
Let K be a compact semi-simple Lie group, and let N be a maximal unipotent subgroup of the complexified group Kc. classify ail the K-invariant Kaehler structures on K-C/N. structure w, let L be the line bundle with connection whose curvature is w. We then study the holomorphic sections of L, which constitute a K-representation space.
Kaehler structures on K-C/(P,P)
(1997-08-01)
Chuah, MK
;
交大名義發表
;
應用數學系
;
National Chiao Tung University
;
Department of Applied Mathematics
Let K be a compact connected semi-simple Lie group, let G = K-C, and let G = KAN be an Iwasawa decomposition. To a given K-invariant Kaehler structure omega on G/N, there corresponds a pre-quantum line bundle L on G/N. Following a suggestion of A.S. Schwarz, in a joint paper with V. Guillemin, we studied its holomorphic sections O(L) as a K-representation space. We defined a K-invariant L-2-structure on O(L), and let H-omega subset of O(L) denote the space of square-integrable holomorphic sections. Then H-omega is a unitary K-representation space, but not all unitary irreducible K-representations occur as subrepresentations of H-omega. This paper serves as a continuation of that work, by generalizing the space considered. Let B be a Borel subgroup containing N, with commutator subgroup (B, B) = N. Instead of working with G/N = G/(B, B), we consider G/(P, P), for all parabolic subgroups P containing B. We carry out a similar construction, and recover in H-omega the unitary irreducible K-representations previously missing. As a result, we use these holomorphic sections to construct a model for K: a unitary K-representation in which every irreducible K-representation occurs with multiplicity one.
Kaehler structures on K-C/(P,P)
(1997-08-01)
Chuah, MK
;
應用數學系
;
Department of Applied Mathematics
Let K be a compact connected semi-simple Lie group, let G = K-C, and let G = KAN be an Iwasawa decomposition. To a given K-invariant Kaehler structure omega on G/N, there corresponds a pre-quantum line bundle L on G/N. Following a suggestion of A.S. Schwarz, in a joint paper with V. Guillemin, we studied its holomorphic sections O(L) as a K-representation space. We defined a K-invariant L-2-structure on O(L), and let H-omega subset of O(L) denote the space of square-integrable holomorphic sections. Then H-omega is a unitary K-representation space, but not all unitary irreducible K-representations occur as subrepresentations of H-omega. This paper serves as a continuation of that work, by generalizing the space considered. Let B be a Borel subgroup containing N, with commutator subgroup (B, B) = N. Instead of working with G/N = G/(B, B), we consider G/(P, P), for all parabolic subgroups P containing B. We carry out a similar construction, and recover in H-omega the unitary irreducible K-representations previously missing. As a result, we use these holomorphic sections to construct a model for K: a unitary K-representation in which every irreducible K-representation occurs with multiplicity one.
Kahler structures and weighted actions on the complex torus
(2000-06-01)
Chuah, MK
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應用數學系
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Department of Applied Mathematics
Let T be the compact real torus, and T-C its complexification. Fix an integral weight alpha, and consider the alpha-weighted T-action on T-C. If omega is a T-invariant Kahler form on T-C, it corresponds to a pre-quantum line bundle L over T-C. Let H-omega be the square-integrable holomorphic sections of L. The weighted T-action lifts to a unitary T-representation on the Hilbert space H-omega, and the multiplicity of its irreducible sub-representations is considered. It is shown that this is controlled by the image of the moment map, as well as the principle that 'quantization commutes with reduction'.
Quantization, reduction, and flag manifolds
(2000-10-01)
Chuah, MK
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應用數學系
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Department of Applied Mathematics
Let K be a compact connected semi-simple Lie group, let G be its complexification, and let G = KAN be an Iwasawa decomposition. Let B be the Borel subgroup containing A and N. Let P be a parabolic subgroup of G containing B, and (P,P) its commutator subgroup. In this paper, we perform geometric quantization and symplectic reduction to the pseudo-kahler forms on the complex homogeneous space GI(P, P). The reduced space is a disjoint union of copies of the flag manifold GIP, and this allows us to study the signatures of the K-invariant pseudo-Kahler forms on GIP via symplectic reduction. We also discuss the connectivity of the reduced space.
Reinhardt domains and toric models
(2003)
Chuah, MK
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應用數學系
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Department of Applied Mathematics
Symplectic induction and semisimple orbits
(2005-06-01)
Chuah, MK
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應用數學系
;
Department of Applied Mathematics
Symplectic induction was first introduced by Weinstein as the symplectic analogue of induced representations, and was further developed by Guillemin and Sternberg. This paper deals with the case where the symplectic manifold in question is a semisimple coadjoint orbit of a Lie group. In this case, the construction is generalized by adding a smooth mapping, in order to obtain various symplectic forms. In particular, when the orbit is elliptic, a study of the complex geometry shows that quantization commutes with induction.
The generalized Borel-Weil theorem and cohomology of G/(P,P)
(1997-03-01)
Chuah, MK
;
應用數學系
;
Department of Applied Mathematics
Let G be a complex semi-simple Lie group. The generalized Borel-Weil theorem computes the cohomology of a compact homogeneous G-space with coefficient in homogeneous line bundle. In this paper, we give an analogous statement via Dolbeault cohomology of the non-compact space G/(P,P) for P subset of G a parabolic subgroup, and (P,P) the commutator subgroup.
The generalized Borel-Weil theorem and cohomology of G/(P,P)
(1997-03-01)
Chuah, MK
;
交大名義發表
;
應用數學系
;
National Chiao Tung University
;
Department of Applied Mathematics
Let G be a complex semi-simple Lie group. The generalized Borel-Weil theorem computes the cohomology of a compact homogeneous G-space with coefficient in homogeneous line bundle. In this paper, we give an analogous statement via Dolbeault cohomology of the non-compact space G/(P,P) for P subset of G a parabolic subgroup, and (P,P) the commutator subgroup.