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- W1495718577 abstract "In this article we describe homomorphisms and extensions of principal series representations. Principal series are certain representations of a semisimple complex Lie algebra g and are objects of the Bernstein-Gelfand- Gelfand-category O. Verma modules and their duals are examples of such principal series representations. Via the equivalence of categories of (3) the principal series representations correspond to Harish-Chandra modules for g g which arise by induction from a minimal parabolic subalgebra of g g. We show that all principal series have one-dimensional endomorphism rings and trivial self-extensions. We also give an explicit example of a higher dimensional homomorphism space between principal series. As an application of these results we prove the existence of character formulae for twisted tilting modules. The twisted tilting modules are some indecomposable objects of O having a ag whose subquotients are principal series modules and for which a certain Ext- vanishing condition holds." @default.
- W1495718577 created "2016-06-24" @default.
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- W1495718577 date "2003-01-01" @default.
- W1495718577 modified "2023-09-22" @default.
- W1495718577 title "Homomorphisms and extensions of principal series representations" @default.
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