Relative BGG sequences; I. Algebra

Andreas Cap; Vladimir Soucek

doi:10.1016/j.jalgebra.2016.06.007

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arXiv · 1510.03331

Relative BGG sequences; I. Algebra

Andreas Cap·Vladimir Soucek

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Abstract

We develop a relative version of Kostant's harmonic theory and use this to prove a relative version of Kostant's theorem on Lie algebra (co)homology. These are associated to two nested parabolic subalgebras in a semisimple Lie algebra. We show how relative homology groups can be used to realize representations with lowest weight in one (regular or singular) affine Weyl orbit. In the regular case, we show how all the weights in the orbit can be realized as relative homology groups (with different coefficients). These results are motivated by applications to differential geometry and the construction of invariant differential operators.

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BibTeX RIS

Andreas Cap, Vladimir Soucek. 2015-10-12. Relative BGG sequences; I. Algebra. https://doi.org/10.1016/j.jalgebra.2016.06.007

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