Anti-commuting varieties
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- by Xinhong Chen and Weiqiang Wang PDF
- Trans. Amer. Math. Soc. 373 (2020), 1597-1617 Request permission
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 (geometric invariant theory) quotient of the anti-commuting variety with respect to the conjugation action of $GL_n$ 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.References
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Additional Information
- Xinhong Chen
- Affiliation: Department of Mathematics, Southwest Jiaotong University, Sichuan 611756, People’s Republic of China
- MR Author ID: 968054
- Email: chenxinhong@swjtu.edu.cn
- Weiqiang Wang
- Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904
- MR Author ID: 339426
- Email: ww9c@virginia.edu
- Received by editor(s): April 14, 2018
- Received by editor(s) in revised form: March 28, 2019
- Published electronically: December 17, 2019
- Additional Notes: The first author was partially supported by NSFC grant No. 11601441 and CSC grant No. 201707005033
The second author was partially supported by an NSF grant DMS-1702254. - © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 1597-1617
- MSC (2010): Primary 16G10
- DOI: https://doi.org/10.1090/tran/8017
- MathSciNet review: 4068275