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Stratification of the discriminant in reflection groups

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Abstract

LetV be a complex vector space and letG⊂GL(V) be a finite unitary reflection group. Letγ:V →V/G be the orbit map. We show that the image of the orbit stratification underγ is determined by a matrix of polynomials called the discriminant matrix, and that this stratification agrees with the stratification ofV/G obtained from logarithmic vector fields tangent to the discriminant hypersurface.

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Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin, 53706, Madison, WI

    Peter Orlik

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  1. Peter Orlik
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This work was supported in part by the National Science Foundation

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Orlik, P. Stratification of the discriminant in reflection groups. Manuscripta Math 64, 377–388 (1989). https://doi.org/10.1007/BF01165826

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  • DOI: https://doi.org/10.1007/BF01165826

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