Principal series representations of infinite-dimensional Lie groups, I: Minimal parabolic subgroups

  • Joseph A. WolfEmail author
Part of the Progress in Mathematics book series (PM, volume 257)


We study the structure of minimal parabolic subgroups of the classical infinite-dimensional real simple Lie groups, corresponding to the classical simple direct limit Lie algebras. This depends on the recently developed structure of parabolic subgroups and subalgebras that are not necessarily direct limits of finite-dimensional parabolics. We then discuss the use of that structure theory for the infinite-dimensional analog of the classical principal series representations. We look at the unitary representation theory of the classical lim-compact groups U(), SO() and Sp() in order to construct the inducing representations, and we indicate some of the analytic considerations in the actual construction of the induced representations.


Principle series representation Infinite-dimensional Lie group Minimal parabolic subgroup 

Mathematics Subject Classification

32L25 22E46 32L10 


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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