The Fine Structure of Translation Functors

Details The Fine Structure of Translation Functors The Fine Structure of Translation Functors

1998-08-28

arxiv.org/abs/math/9808117v1

Representation Theory 3 (1999), pp. 223-249. An Electronic Journal of the AMS.

Mathematics

Representation Theory

28 pages, LaTeX

Scientific paper

Let E be a simple finite dimensional representation of a semisimple Lie algebra with extremal weight nu and choose nonzero e in E_{nu}. Let M(tau) be the Verma module with highest weight tau and v_{tau} in M(tau)_{tau} its canonical generator. We investigate the projection of e \otimes v_{tau} in E \otimes M(tau) on the central character chi(tau + nu). This is a rational function in tau and we calculate its poles and zeros. We then apply this result in order to compare translation functors.

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