A remark on quiver varieties and Weyl groups
Andrea Maffei (2002)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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In this paper we define an action of the Weyl group on the quiver varieties with generic .
Andrea Maffei (2002)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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In this paper we define an action of the Weyl group on the quiver varieties with generic .
Pavel Etingof, Wee Liang Gan, Victor Ginzburg, Alexei Oblomkov (2007)
Publications Mathématiques de l'IHÉS
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The main result of the paper is a natural construction of the spherical subalgebra in a symplectic reflection algebra associated with a wreath-product in terms of quantum hamiltonian reduction of an algebra of differential operators on a representation space of an extended Dynkin quiver. The existence of such a construction has been conjectured in [EG]. We also present a new approach to reflection functors and shift functors for generalized preprojective algebras and symplectic reflection...
Werner, Annette (2001)
Documenta Mathematica
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Tomasz Przebinda (2006)
Open Mathematics
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In this paper we identify a real reductive dual pair of Roger Howe with an Ordinary Classical Lie supergroup. In these terms we describe the semisimple orbits of the dual pair in the symplectic space, a slice through a semisimple element of the symplectic space, an analog of a Cartan subalgebra, the corresponding Weyl group and the corresponding Weyl integration formula.
Hill, David, Sussan, Joshua (2010)
International Journal of Mathematics and Mathematical Sciences
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Fedor Bogomolov, Christian Böhning, Hans-Christian Graf von Bothmer (2012)
Open Mathematics
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Let G be one of the groups SLn(ℂ), Sp2n (ℂ), SOm(ℂ), Om(ℂ), or G 2. For a generically free G-representation V, we say that N is a level of stable rationality for V/G if V/G × ℙN is rational. In this paper we improve known bounds for the levels of stable rationality for the quotients V/G. In particular, their growth as functions of the rank of the group is linear for G being one of the classical groups.
van der Geer, G., Katsura, T. (2003)
Documenta Mathematica
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David Ginzburg, Stephen Rallis, David Soudry (1998)
Bulletin de la Société Mathématique de France
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Ben Moonen (2004)
Annales de l’institut Fourier
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We study the Ekedahl-Oort stratification on moduli spaces of PEL type. The strata are indexed by the classes in a Weyl group modulo a subgroup, and each class has a distinguished representative of minimal length. The main result of this paper is that the dimension of a stratum equals the length of the corresponding Weyl group element. We also discuss some explicit examples.