Two results on equations of nilpotent orbits
Author:
Jerzy Weyman
Journal:
J. Algebraic Geom. 11 (2002), 791-800
DOI:
https://doi.org/10.1090/S1056-3911-02-00335-1
Published electronically:
June 17, 2002
MathSciNet review:
1910987
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Abstract |
References |
Additional Information
Abstract: Let $\Phi$ be a generic $n\times n$ matrix over a field $K$ of characteristic zero. In this note I find the set of minimal generators of the ideal generated by the entries of the matrix $\Phi ^e$ and by the coefficients of the characteristic polynomial of $\Phi$. In particular, I show that this ideal is reduced. For $e=2$ the result is characteristic free.
[FW]FW T. Fukui, J. Weyman, Cohen-Macaulay properties of Thom-Boardman strata. I. Morin’s ideal. Proc. London Math. Soc. (3) 80 (2000), no. 2, 257-303.
[J]J G.D. James, Representations of the Symmetric Group, Lect. Notes Maths. 628, Springer, 1978.
[Ja]Ja J.C. Jantzen, Representations of Algebraic Groups, Academic Press, 1987.
[MVK]MVK V.B. Mehta, W. Van der Kallen, A simultaneous Frobenius splitting for closures of conjugacy classes of nilpotent matrices, Compositio Math. 84 (1992), 211-221.
[PR]PR G. Pappas, M. Rapoport, Local models in the ramified case. I. The EL-case, preprint, 2000.
[S]S E. Strickland, On the variety of projectors, J. Algebra 106 (1987), 135-147.
[W]W J. Weyman, The equations of conjugacy classes of nilpotent matrices, Invent. Math. 98, 229-245 (1989).
[FW]FW T. Fukui, J. Weyman, Cohen-Macaulay properties of Thom-Boardman strata. I. Morin’s ideal. Proc. London Math. Soc. (3) 80 (2000), no. 2, 257-303.
[J]J G.D. James, Representations of the Symmetric Group, Lect. Notes Maths. 628, Springer, 1978.
[Ja]Ja J.C. Jantzen, Representations of Algebraic Groups, Academic Press, 1987.
[MVK]MVK V.B. Mehta, W. Van der Kallen, A simultaneous Frobenius splitting for closures of conjugacy classes of nilpotent matrices, Compositio Math. 84 (1992), 211-221.
[PR]PR G. Pappas, M. Rapoport, Local models in the ramified case. I. The EL-case, preprint, 2000.
[S]S E. Strickland, On the variety of projectors, J. Algebra 106 (1987), 135-147.
[W]W J. Weyman, The equations of conjugacy classes of nilpotent matrices, Invent. Math. 98, 229-245 (1989).
Additional Information
Jerzy Weyman
Affiliation:
Department of Mathematics, Northeastern University, Boston, Massachusetts 02115-5096
MR Author ID:
182230
ORCID:
0000-0003-1923-0060
Email:
j.weyman@neu.edu
Received by editor(s):
August 30, 2000
Published electronically:
June 17, 2002
Additional Notes:
Supported by NSF grant DMS 9700884
