Abstract
We consider parabolic subgroups of a general linear group over an algebraically closed field k whose Levi part has exactly t factors. By a classical theorem of Richardson, the nilradical of a parabolic subgroup P has an open dense P-orbit. In the complement to this dense orbit, there are infinitely many orbits as soon as the number t of factors in the Levi part is ≥6. In this paper, we describe the irreducible components of the complement. In particular, we show that there are at most t − 1 irreducible components. We are also able to determine their codimensions.
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This research was supported through the programme “Research in Pairs” by the Mathematisches Forschungsinstitut Oberwolfach in 2009. K. Baur was supported by SNF. L. Hille was supported by the DFG priority program SPP 1388 representation theory.
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Baur, K., Hille, L. On the complement of the Richardson orbit. Math. Z. 272, 31–49 (2012). https://doi.org/10.1007/s00209-011-0920-9
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DOI: https://doi.org/10.1007/s00209-011-0920-9