Partially harmonic forms and models of H-series

作者：Chuah Meng Kiat^*

来源：Journal of Functional Analysis, 2014, 266(5): 2740-2764.

DOI：10.1016/j.jfa.2013.12.013

• Reductive Lie group
• H-series
• Geometric quantization
• Partially harmonic form
• Moment map

Let G be a real reductive Lie group, let H = TA be the identity component of a Cartan subgroup, and let h be the corresponding Cartan subgroup. This leads to a parabolic subgroup of G whose identity component is MAN. The unitary G-representations induced by MAN are known as the H-series. We study symplectic geometry of G x h and apply geometric quantization to construct unitary G-representations by partially harmonic forms. They are direct integrals of the H-series, indexed by the image of the moment map. We also perform symplectic reduction and symplectic induction, and consider their analogues in representation theory via geometric quantization.

• 出版日期2014-3-1
• 单位清华大学