arXiv subjects

Meng-Kiat Chuah

Publications and source records attributed to Meng-Kiat Chuah.

6 recordsLinked to original sources

arXiv2026

Super Kähler structures on the complex Abelian Lie supergroups

Let $G$ be a real Abelian Lie supergroup, let $M$ be its complexification. We classify the $G$-invariant super Kähler forms on $M$. For the super Kähler forms with Hamiltonian actions, we extend the scheme of geometric quantization to the super setting and construct unitary $G$-representations. We show that the irreducible representations that occur in these unitary representations are governed by the image of the moment maps of super Kähler forms. As an application, we construct a Gelfand model of $G$, namely a unitary $G$-representation in which every unitary irreducible representation occurs exactly once.

math.DG↗

arXiv2024

Geometric quantization and unitary highest weight Harish-Chandra supermodules

Geometric quantization transforms a symplectic manifold with Lie group action to a unitary representation. In this article, we extend geometric quantization to the super setting. We consider real forms of contragredient Lie supergroups with compact Cartan subgroups, and study their actions on some pseudo-Kähler supermanifolds. We construct their unitary representations in terms of sections of some line bundles. These unitary representations contain highest weight Harish-Chandra supermodules, whose occurrences depend on the image of the moment map. As a result, we construct a Gelfand model of highest weight Harish-Chandra supermodules. We also perform symplectic reduction, and show that quantization commutes with reduction.

math.RT↗

arXiv2022

Partial Dirac Cohomology and Tempered Representations

The tempered representations of a real reductive Lie group $G$ are naturally partitioned into series associated with conjugacy classes of Cartan subgroups $H$ of $G$. We define partial Dirac cohomology, apply it for geometric construction of various models of these $H$--series representations, and show how this construction fits into the framework of geometric quantization and symplectic reduction.

math.RT↗

arXiv2022

Affine Vogan Diagrams and Symmetric Pairs

We introduce the affine Vogan diagrams of complex simple Lie algebras. These are generalizations of Vogan diagrams, and we study the involutions represented by them. We apply these diagrams to study the symmetric pairs, in particular the associated and symplectic symmetric pairs.

math.RT↗

arXiv2022

Outer Automorphism Groups of Simple Lie Algebras and Symmetries of Painted Diagrams

For a real semisimple Lie algebra, we consider its automorphism group quotient by its identity component. This is known as the outer automorphism group. In this article, we compute the outer automorphism groups of all real semisimple Lie algebras.

math.RT↗

arXiv1996

Kaehler structures on Kc/(P,P)

Let K be a compact semi-simple Lie group. We classify K-invariant Kaehler structures on the space Kc/(P,P), where Kc is the complexification of K, P is a parabolic subgroup of Kc, and (P,P) the commutator subgroup. For each Kaehler structure, we study its moment map and associated pre-quantum line bundle for geometric quantization. Some holomorphic sections of the line bundle form a unitary K-representation space, and we study the multiplicity of its irreducible subrepresentations.

dg-ga↗