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Dixmier's Problem for Verma and Principal Series Submodules
Author(s) -
Joseph A.
Publication year - 1979
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-20.2.193
Subject(s) - series (stratigraphy) , principal (computer security) , verma module , mathematics , point (geometry) , algebra over a field , arithmetic , pure mathematics , computer science , lie algebra , geometry , paleontology , biology , operating system
The starting point of this paper is Dixmier's problem relating Verma modules to principal series submodules [5; Probleme 30]. Not only is this problem completely solved, but this relationship is given a very precise form. This allows, for example, one to use the results of Jantzen to determine the multiplicities in the Jordan‐Hölder series for the principal series of a complex semisimple Lie group.