Dirac operators and Lie algebra cohomology

By Jing Huang, Pavle Pandvzi'c, David.Renard. 2005

48 citations recorded by the source corpus.

Dirac cohomology is a new tool to study unitary and admissible represen- tations of semisimple Lie groups. It was introduced by Vogan and further studied by Kostant and ourselves (V2), (HP1), (K4). The aim of this paper is to study the Dirac cohomology for the Kostant cubic Dirac operator and its relation to Lie algebra coho- mology. We show that the Dirac cohomology coincides with the corresponding nilpotent Lie algebra cohomology in many cases, while in general it has better algebraic behavior and it is more accessible for calculation.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a2b57668004a9b96b9524603f3b62062d66d8790

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Yifang Kang
2. Pavle Pandžić
3. Jing Huang

In Mathematical Physics

1. Yifang Kang
2. Pavle Pandžić
3. Jing Huang

Citations in the corpus

• Dirac Cohomology of some Harish-Chandra Modules (2009, background): “Namely, by a result of [ HPR , Theorem 7.11] their Dirac cohomology is up to a twist by a one-dimensional character isomorphic to the p + -cohomology, and the latter”