Dirac Operators and Nilpotent Lie Algebra Cohomology

Part of the Mathematics: Theory & Applications book series (MTA)


Let g be a complex reductive Lie algebra with an invariant symmetric bilinear form B, equal to the Killing form on the semisimple part of g. In this chapter we consider a parabolic subalgebra q = lu of g, with unipotent radical u and a Levi subalgebra l. We will denote by
$$ \bar q = \mathfrak{l} \oplus \bar u $$
the opposite parabolic subalgebra. Here the bar notation does not mean complex conjugation in general, but it will be a conjugation in the cases we will study the most, so the notation is convenient.


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© Birkhäuser Boston 2006

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