Premium
Integral geometry for \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathcal {D}}$\end{document} ‐modules on dual flag manifolds and generalized Verma modules
Author(s) -
Marastoni Corrado
Publication year - 2013
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201200149
Subject(s) - mathematics , flag (linear algebra) , verma module , generalized flag variety , pure mathematics , representation theory , dual (grammatical number) , product (mathematics) , orbit (dynamics) , algebra over a field , group (periodic table) , geometry , lie group , lie algebra , physics , quantum mechanics , engineering , aerospace engineering , art , literature
Abstract Given a pair of dual generalized flag manifolds of a semisimple algebraic group, we show that the integral transform between them given by the open orbit in their product is an equivalence. We also describe the links of this problem with the structure of generalized Verma modules, and how the above construction can be applied to the representation theory of real forms of the group.