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},
pages = {91--155},
publisher = {Springer},
volume = {105},
year = {2007},
doi = {10.1007/s10240-007-0005-9},
zbl = {1188.16010},
language = {en},
url = {http://www.numdam.org/articles/10.1007/s10240-007-0005-9/}
}
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 SP - 91 EP - 155 VL - 105 PB - Springer UR - http://www.numdam.org/articles/10.1007/s10240-007-0005-9/ DO - 10.1007/s10240-007-0005-9 LA - en ID - PMIHES_2007__105__91_0 ER -
%0 Journal Article %A Etingof, Pavel %A Gan, Wee Liang %A Ginzburg, Victor %A Oblomkov, Alexei %T Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products %J Publications Mathématiques de l'IHÉS %D 2007 %P 91-155 %V 105 %I Springer %U http://www.numdam.org/articles/10.1007/s10240-007-0005-9/ %R 10.1007/s10240-007-0005-9 %G en %F 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, Tome 105 (2007), pp. 91-155. doi : 10.1007/s10240-007-0005-9. http://www.numdam.org/articles/10.1007/s10240-007-0005-9/
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