Geodesic
On category $\mathcal{O}$ for cyclotomic rational Cherednik algebras
Journal of the European Mathematical Society, Tome 16 (2014) no. 5, pp. 1017-1079.

Voir la notice de l'article provenant de la source EMS Press

We study equivalences for category Op​ of the rational Cherednik algebras Hp​ of type Gl​(n)=(μl​)n⋊Sn​: a highest weight equivalence between Op​ and Oσ(p)​ for σ∈Sl​ and an action of Sl​ on an explicit non-empty Zariski open set of parameters p; a derived equivalence between Op​ and Op′​ whenever p and p′ have integral difference; a highest weight equivalence between Op​ and a parabolic category O for the general linear group, under a non-rationality assumption on the parameter p. As a consequence, we confirm special cases of conjectures of Etingof and of Rouquier.
DOI : 10.4171/jems/454
Classification : 16-XX, 00-XX, 17-XX
Keywords: Cherednik algebra, category O, derived category, deformation quantization, categorification 
@article{JEMS_2014_16_5_a4,
     author = {Iain G. Gordon and Ivan Losev},
     title = {On category $\mathcal{O}$ for cyclotomic rational {Cherednik} algebras},
     journal = {Journal of the European Mathematical Society},
     pages = {1017--1079},
     publisher = {mathdoc},
     volume = {16},
     number = {5},
     year = {2014},
     doi = {10.4171/jems/454},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/454/}
}
TY  - JOUR
AU  - Iain G. Gordon
AU  - Ivan Losev
TI  - On category $\mathcal{O}$ for cyclotomic rational Cherednik algebras
JO  - Journal of the European Mathematical Society
PY  - 2014
SP  - 1017
EP  - 1079
VL  - 16
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/454/
DO  - 10.4171/jems/454
ID  - JEMS_2014_16_5_a4
ER  - 
%0 Journal Article
%A Iain G. Gordon
%A Ivan Losev
%T On category $\mathcal{O}$ for cyclotomic rational Cherednik algebras
%J Journal of the European Mathematical Society
%D 2014
%P 1017-1079
%V 16
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/454/
%R 10.4171/jems/454
%F JEMS_2014_16_5_a4
Iain G. Gordon; Ivan Losev. On category $\mathcal{O}$ for cyclotomic rational Cherednik algebras. Journal of the European Mathematical Society, Tome 16 (2014) no. 5, pp. 1017-1079. doi : 10.4171/jems/454. http://geodesic.mathdoc.fr/articles/10.4171/jems/454/

Cité par Sources :