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This article is cited in 1 scientific paper (total in 1 paper)
Partial normalizations of Coxeter arrangements and discriminants
Michel Grangera, David Mondb, Mathias Schulzec a Université d'Angers, Département de Mathématiques, LAREMA, CNRS UMR no 6093, 2 Bd Lavoisier, 49045 Angers, France
b Mathematics Institute, University of Warwick, Coventry CV47AL, England
c Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, United States
Abstract:
We study natural partial normalization spaces of Coxeter arrangements and discriminants and relate their geometry to representation theory. The underlying ring structures arise from Dubrovin's Frobenius manifold structure which is lifted (without unit) to the space of the arrangement. We also describe an independent approach to these structures via duality of maximal Cohen–Macaulay fractional ideals. In the process, we find 3rd order differential relations for the basic invariants of the Coxeter group. Finally, we show that our partial normalizations give rise to new free divisors.
Key words and phrases:
Coxeter group, logarithmic vector field, free divisor.
Received: September 1, 2011; in revised form January 20, 2012
Citation:
Michel Granger, David Mond, Mathias Schulze, “Partial normalizations of Coxeter arrangements and discriminants”, Mosc. Math. J., 12:2 (2012), 335–367
Linking options:
https://www.mathnet.ru/eng/mmj470 https://www.mathnet.ru/eng/mmj/v12/i2/p335
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