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Twisted Verma modules
H. H. Andersen and N. Lauritzen
ABSTRACT Using principal series Harish-Chandra modules, local cohomology
with support in Schubert cells and twisting functors we construct certain modules
parametrized by the Weyl group and a highest weight in the subcategory O of
the category of representations of a complex semisimple Lie algebra. These are in
a sense modules between a Verma module and its dual. We prove that the three
di erent approaches lead to the same modules. Moreover, we demonstrate that
they possess natural Jantzen type ltrations with corresponding sum formulae.
Let g be a nite dimensional complex semisimple Lie algebra with a
Cartan subalgebra h  g and Weyl group W . In this paper we consider
twisted Verma modules. These are in a sense representations between a
Verma module and its dual. Fix a highest weight  2 h  . The twisted
Verma modules M w () corresponding to  are parametrized by the Weyl
group W . They have the same formal character as the Verma module M()
(but in general not the same module structure). In the aĆne Kac-Moody
setting these modules (turning out to be Wakimoto modules) have been
studied by Feigin and Frenkel [6].

  

Source: Andersen, Henning Haahr - Department of Mathematics, Aarhus Universitet

 

Collections: Mathematics