Journal of Algebraic Geometry Journal of Algebraic Geometry

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Two results on equations of nilpotent orbits

Author(s): Jerzy Weyman
Journal: J. Algebraic Geom. 11 (2002), 791-800.
Posted: June 17, 2002
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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.

References:

[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]
G.D. James, Representations of the Symmetric Group, Lect. Notes Maths. 628, Springer, 1978.

[Ja]
J.C. Jantzen, Representations of Algebraic Groups, Academic Press, 1987.

[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]
G. Pappas, M. Rapoport, Local models in the ramified case. I. The EL-case, preprint, 2000.

[S]
E. Strickland, On the variety of projectors, J. Algebra 106 (1987), 135-147.

[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
Email: j.weyman@neu.edu

PII: S 1056-3911(02)00335-1
Received by editor(s): August 30, 2000
Posted: June 17, 2002
Additional Notes: Supported by NSF grant DMS 9700884

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