scholarly journals Domains of holomorphy for irreducible unitary representations of simple Lie groups

2007 ◽  
Vol 172 (2) ◽  
pp. 277-288 ◽  
Author(s):  
Bernhard Krötz
Keyword(s):  
Lie Groups ◽  
Unitary Representations ◽  
Simple Lie Groups ◽  
Irreducible Unitary Representations ◽  
Domains Of Holomorphy

scholarly journals Unitary representations with Dirac cohomology: A finiteness result for complex Lie groups

2020 ◽  
Vol 32 (4) ◽  
pp. 941-964 ◽  
Author(s):  
Jian Ding ◽  
Chao-Ping Dong
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Equivalence Classes ◽  
Unitary Representations ◽  
Parabolic Subgroups ◽  
Dirac Cohomology ◽  
Finiteness Result ◽  
Irreducible Unitary Representations ◽  
Cohomological Induction ◽  
Good Range

AbstractLet G be a connected complex simple Lie group, and let {\widehat{G}^{\mathrm{d}}} be the set of all equivalence classes of irreducible unitary representations with non-vanishing Dirac cohomology. We show that {\widehat{G}^{\mathrm{d}}} consists of two parts: finitely many scattered representations, and finitely many strings of representations. Moreover, the strings of {\widehat{G}^{\mathrm{d}}} come from {\widehat{L}^{\mathrm{d}}} via cohomological induction and they are all in the good range. Here L runs over the Levi factors of proper θ-stable parabolic subgroups of G. It follows that figuring out {\widehat{G}^{\mathrm{d}}} requires a finite calculation in total. As an application, we report a complete description of {\widehat{F}_{4}^{\mathrm{d}}}.

scholarly journals One more method to construct the irreducible unitary representations of nipotent Lie groups

1986 ◽  
Vol 40 (1) ◽  
pp. 89-94
Author(s):  
A. A. Astaneh
Keyword(s):  
Lie Groups ◽  
Lie Algebra ◽  
Lie Group ◽  
Unitary Representations ◽  
Irreducible Representations ◽  
Nilpotent Lie Group ◽  
Irreducible Unitary Representations ◽  
Simply Connected

AbstractIn this paper one more canonical method to construct the irreducible unitary representations of a connected, simply connected nilpotent Lie group is introduced. Although we used Kirillov' analysis to deduce this procedure, the method obtained differs from that of Kirillov's, in that one does not need to consider the codjoint representation of the group in the dual of its Lie algebra (in fact, neither does one need to consider the Lie algebra of the group, provided one knows certain connected subgroups and their characters). The method also differs from that of Mackey's as one only needs to induce characters to obtain all irreducible representations of the group.

Sign in / Sign up

Export Citation Format

Share Document