English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider the conjugation-action of an arbitrary upper-block parabolicsubgroup of GL_n(C) on the variety of x-nilpotent complex matrices. We obtain acriterion as to whether the action admits a finite number of orbits and specifya system of representatives for the orbits in the finite case of 2-nilpotentmatrices. Furthermore, we give a set-theoretic description of their closuresand specify the minimal degenerations in detail for the action of the Borelsubgroup. Concerning the action on the nilpotent cone, we obtain a genericnormal form of the orbits which yields a U-normal form as well, here U is thestandard unipotent subgroup. We describe generating (semi-) invariants for theBorel semi-invariant ring as well as for the U-invariant ring. The latter isdescribed in more detail in terms of algebraic quotients by a special toricvariety closely related.

Conjugation on varieties of nilpotent matrices