# On category $\mathcal{O}$ for cyclotomic rational Cherednik algebras

Journal of the European Mathematical Society (2014)

- Volume: 016, Issue: 5, page 1017-1079
- ISSN: 1435-9855

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topGordon, Iain G., and Losev, Ivan. "On category $\mathcal {O}$ for cyclotomic rational Cherednik algebras." Journal of the European Mathematical Society 016.5 (2014): 1017-1079. <http://eudml.org/doc/277747>.

@article{Gordon2014,

abstract = {We study equivalences for category $\mathcal \{O\}_p$ of the rational Cherednik algebras $\textbf \{H\}_p$ of type $G_\{\ell \}(n) = (\mu _\{\ell \})^n\rtimes \mathfrak \{S\}_n$: a highest weight equivalence between $\mathcal \{O\}_p$ and $\mathcal \{O\}_\{\sigma (p)\}$ for $\sigma \in \mathfrak \{S\}_\{\ell \}$ and an action of $\mathfrak \{S\}_\{\ell \}$ on an explicit non-empty Zariski open set of parameters $p$; a derived equivalence between $\mathcal \{O\}_p$ and $\mathcal \{O\}_\{p^\{\prime \}\}$ whenever $p$ and $p^\{\prime \}$ have integral difference; a highest weight equivalence between $\mathcal \{O\}_p$ and a parabolic category $\mathcal \{O\}$ 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.},

author = {Gordon, Iain G., Losev, Ivan},

journal = {Journal of the European Mathematical Society},

keywords = {Cherednik algebra; category $\mathcal \{O\}$; derived category; deformation quantization; categorification; Cherednik algebra; category ; derived category; deformation quantization; categorification},

language = {eng},

number = {5},

pages = {1017-1079},

publisher = {European Mathematical Society Publishing House},

title = {On category $\mathcal \{O\}$ for cyclotomic rational Cherednik algebras},

url = {http://eudml.org/doc/277747},

volume = {016},

year = {2014},

}

TY - JOUR

AU - Gordon, Iain G.

AU - Losev, Ivan

TI - On category $\mathcal {O}$ for cyclotomic rational Cherednik algebras

JO - Journal of the European Mathematical Society

PY - 2014

PB - European Mathematical Society Publishing House

VL - 016

IS - 5

SP - 1017

EP - 1079

AB - We study equivalences for category $\mathcal {O}_p$ of the rational Cherednik algebras $\textbf {H}_p$ of type $G_{\ell }(n) = (\mu _{\ell })^n\rtimes \mathfrak {S}_n$: a highest weight equivalence between $\mathcal {O}_p$ and $\mathcal {O}_{\sigma (p)}$ for $\sigma \in \mathfrak {S}_{\ell }$ and an action of $\mathfrak {S}_{\ell }$ on an explicit non-empty Zariski open set of parameters $p$; a derived equivalence between $\mathcal {O}_p$ and $\mathcal {O}_{p^{\prime }}$ whenever $p$ and $p^{\prime }$ have integral difference; a highest weight equivalence between $\mathcal {O}_p$ and a parabolic category $\mathcal {O}$ 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.

LA - eng

KW - Cherednik algebra; category $\mathcal {O}$; derived category; deformation quantization; categorification; Cherednik algebra; category ; derived category; deformation quantization; categorification

UR - http://eudml.org/doc/277747

ER -

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