Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products
Publications Mathématiques de l'IHÉS, Volume 105 (2007), p. 91-155

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.

@article{PMIHES_2007__105__91_0,
     author = {Etingof, Pavel and Gan, Wee Liang and Ginzburg, Victor and Oblomkov, Alexei},
     title = {Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     publisher = {Springer},
     volume = {105},
     year = {2007},
     pages = {91-155},
     doi = {10.1007/s10240-007-0005-9},
     zbl = {1188.16010},
     zbl = {pre05223502},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_2007__105__91_0}
}
Etingof, Pavel; Gan, Wee Liang; Ginzburg, Victor; Oblomkov, Alexei. Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products. Publications Mathématiques de l'IHÉS, Volume 105 (2007) pp. 91-155. doi : 10.1007/s10240-007-0005-9. http://www.numdam.org/item/PMIHES_2007__105__91_0/

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