Anti-commuting varieties

Abstract

We study the anti-commuting variety which consists of pairs of anti-commuting $n\times n$ matrices. We provide an explicit description of its irreducible components and their dimensions. The GIT quotient of the anti-commuting variety with respect to the conjugation action of $G{L}_n$ is shown to be of pure dimension $n$. We also show the semi-nilpotent anti-commuting variety (in which one matrix is required to be nilpotent) is of pure dimension $n^2$ and describe its irreducible components.

arXiv commentv2, 22 pages, simplified presentation and improved exposition

References in corpus (3)

• Quivers with loops and generalized crystals
• Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type
• Stability of the centers of group algebras of $G{L}_n(q)$

Cited by in corpus (1)

• Stability of the centers of group algebras of $G{L}_n(q)$