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Non-Reductive Conjugation on the Nilpotent Cone

Abstract

We consider the conjugation-action of an arbitrary upper-block parabolic subgroup of GL n (C), especially of the Borel subgroup B and of the standard unipotent subgroup U of the latter on the nilpotent cone of complex nilpotent matrices. We obtain generic normal forms of the orbits and describe generating (semi-) invariants for the Borel semi-invariant ring as well as for the U-invariant ring. The latter is described in more detail in terms of algebraic quotients by a special toric variety closely related. The study of a GIT-quotient for the Borel-action is initiated.

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Correspondence to Magdalena Boos.

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Boos, M. Non-Reductive Conjugation on the Nilpotent Cone. Algebr Represent Theor 17, 1683–1706 (2014). https://doi.org/10.1007/s10468-014-9465-z

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Keywords

  • Parabolic orbits in the nilpotent cone
  • Semiinvariants
  • Generic normal form
  • (Semi-)invariant ring

Mathematics Subject Classifications (2010)

  • 14R20
  • 16W22