Parabolic orbits of $2$-nilpotent elements for classical groups

Magdalena Boos; Giovanni Cerulli Irelli; Francesco Esposito

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arXiv · 1802.06425

Parabolic orbits of $2$-nilpotent elements for classical groups

Magdalena Boos·Giovanni Cerulli Irelli·Francesco Esposito

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Abstract

We consider the conjugation-action of the Borel subgroup of the symplectic or the orthogonal group on the variety of nilpotent complex elements of nilpotency degree $2$ in its Lie algebra. We translate the setup to a representation-theoretic context in the language of a symmetric quiver algebra. This makes it possible to provide a parametrization of the orbits via a combinatorial tool that we call symplectic/orthogonal oriented link patterns. We deduce information about numerology. We then generalize these classifications to standard parabolic subgroups for all classical groups. Finally, our results are restricted to the nilradical.

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BibTeX RIS

Magdalena Boos, Giovanni Cerulli Irelli, Francesco Esposito. 2019-02-08. Parabolic orbits of $2$-nilpotent elements for classical groups. https://arxiv.org/abs/1802.06425

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