Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products

Pavel Etingof; Wee Liang Gan; Victor Ginzburg; Alexei Oblomkov

Publications Mathématiques de l'IHÉS (2007)

  • Volume: 105, page 91-155
  • ISSN: 0073-8301

Abstract

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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 algebras associated with wreath-products.

How to cite

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Etingof, Pavel, et al. "Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products." Publications Mathématiques de l'IHÉS 105 (2007): 91-155. <http://eudml.org/doc/104226>.

@article{Etingof2007,
abstract = {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 algebras associated with wreath-products.},
author = {Etingof, Pavel, Gan, Wee Liang, Ginzburg, Victor, Oblomkov, Alexei},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {spherical subalgebras; symplectic reflection algebras; wreath products; quantum Hamiltonian reductions; algebras of differential operators; representation spaces; extended Dynkin quivers; reflection functors; generalized preprojective algebras},
language = {eng},
pages = {91-155},
publisher = {Springer},
title = {Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products},
url = {http://eudml.org/doc/104226},
volume = {105},
year = {2007},
}

TY - JOUR
AU - Etingof, Pavel
AU - Gan, Wee Liang
AU - Ginzburg, Victor
AU - Oblomkov, Alexei
TI - Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products
JO - Publications Mathématiques de l'IHÉS
PY - 2007
PB - Springer
VL - 105
SP - 91
EP - 155
AB - 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 algebras associated with wreath-products.
LA - eng
KW - spherical subalgebras; symplectic reflection algebras; wreath products; quantum Hamiltonian reductions; algebras of differential operators; representation spaces; extended Dynkin quivers; reflection functors; generalized preprojective algebras
UR - http://eudml.org/doc/104226
ER -

References

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