# 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

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topEtingof, 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 -

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