On category O for cyclotomic rational Cherednik algebras

By I. Gordon, I. Losev. 2011

65 citations recorded by the source corpus.

We study equivalences for category O_p of the rational Cherednik algebras H_p of type G_l(n) = \mu_l^n\rtimes S_n: a highest weight equivalence between O_p and O_{\sigma(p)} for \sigma\in S_l and an action of S_l on a non-empty Zariski open set of parameters p; a derived equivalence between O_p and O_{p'} whenever p and p' have integral difference; a highest weight equivalence between O_p 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/73dce690d78aae818bf4bc35680fc0ecf089c8a0

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In Algebra and Number Theory

1. I. Losev
2. Ben Webster
3. E. Gorsky
4. Pavel Etingof
5. T. Nevins
6. Kevin McGerty
7. I. Gordon
8. V. Ginzburg

In Geometry and Topology

1. I. Losev
2. Ben Webster
3. E. Gorsky
4. T. Nevins
5. Kevin McGerty
6. Pavel Etingof
7. I. Gordon
8. V. Ginzburg

In Mathematical Physics

1. I. Losev
2. Ben Webster
3. E. Gorsky
4. T. Nevins
5. Kevin McGerty
6. Pavel Etingof
7. I. Gordon
8. V. Ginzburg

Citations in the corpus

• Derived equivalence for quantum symplectic resolutions (2011, methodology): “erednik algebra. Their equivalences are established by completely different means – namely the quantisation of the exceptional objects constructed by [BK] (therein called “weakly Procesi bundles”). In [GL], such derived equivalences are used in a detailed study of the category Orepresentations of the”
• Representations of Rational Cherednik algebras with minimal support and torus knots (2013, background): “nce of categories for c>0. Corollary 6.12. One has Shm n (K• m,n) ∼=K• m+n,n. Proof. This follows from Proposition 6.11 and the fact that the shift functor maps Verma modules to Verma modules, see [GL]. Namely, Lemma 4.3.2 in [GL] says that if a category is equipped with two highest weight struct”
• ROUQUIER’S CONJECTURE AND DIAGRAMMATIC ALGEBRA (2013, background): “the diagram of ν, its x-coordinate is b m + g(j − i), that is, the x-coordinate of the center of the box when partitions are drawn as we have specified. This coincides with the s-shifted content as in [GL] if we choose g = 1 and s i = b m. Definition2.12. Theweighteddominanceorderonmultipartitionsfora”