The degree of the discriminant of irreducible representations

Fehér, L.; Némethi, A.; Rimányi, R.

doi:10.1090/S1056-3911-08-00483-9

Authors: L. M. Fehér, A. Némethi and R. Rimányi
Journal: J. Algebraic Geom. 17 (2008), 751-780
DOI: https://doi.org/10.1090/S1056-3911-08-00483-9
Published electronically: February 19, 2008
MathSciNet review: 2424926
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Abstract | References | Additional Information

Abstract: We present a formula for the degree of the discriminant of irreducible representations of a Lie group, in terms of the roots of the group and the highest weight of the representation. The proof uses equivariant cohomology techniques, namely, the theory of Thom polynomials, and a new method for their computation. We study the combinatorics of our formulas in various special cases.

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Additional Information

L. M. Fehér
Affiliation: Department of Analysis, ELTE TTK, Pázmány P. s. 1/c, 1117 Budapest, Hungary
Email: lfeher@renyi.hu

A. Némethi
Affiliation: Renyi Institute of Mathematics, 13–15 Reáltanoda u. 1053 Budapest, Hungary; and Ohio State University, Columbus, Ohio 43210-1101
Email: nemethi@renyi.hu, nemethi@math.ohio-state.edu

R. Rimányi
Affiliation: Department of Mathematics, University of North Carolina, CB #3250 Phillips Hall, Chapel Hill, North Carolina 27599
Email: rimanyi@email.unc.edu

Received by editor(s): August 29, 2006
Published electronically: February 19, 2008
Additional Notes: The first and third authors were supported by OTKA T046365MAT. The second author was supported by NSF grant DMS-0304759 and OTKA 42769/46878. The third author was supported by NSF grant DMS-0405723