Symplectic reflection algebras

By I. Gordon. 2007

146 citations recorded by the source corpus.

We survey recent results on the representation theory of symplectic reflection algebras, focusing particularly on connections with symplectic quotient singularities and their resolutions, spaces of representations of quivers, and on category O.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0c33aa5d324d4579d24e94b4bf125d35c89eda25

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In Geometry and Topology

1. I. Gordon
2. Stephen Griffeth
3. I. Losev
4. V. Ginzburg
5. Alexei Oblomkov
6. Masaki Kashiwara
7. Raphaël Rouquier
8. R. Berger

In Mathematical Physics

1. I. Gordon
2. I. Losev
3. Stephen Griffeth
4. V. Ginzburg
5. Alexei Oblomkov
6. Raphaël Rouquier
7. Masaki Kashiwara
8. Pavel Etingof

Citations in the corpus

• Azumaya loci and discriminant ideals of PI algebras (2017, background): “(3) (special case of (1)) noetherian prime regular group algebras satisfying a polynomial identity; that is, group algebras KG of finitely generated abelian-by- finite groups G with no non-trivial finite normal subgroups and with no elements of order charK; (4) (special case of (1)) quantized envelo”
• Orthogonal functions generalizing Jack polynomials (2007, background): “The PBW theorem (see (8), (12), (28), and (19)) for H asserts that as F -vector spaces, (4.”
• Higher symplectic reflection algebras and non-homogeneous N-Koszul property (2005, background): “Then the symplectic reflection algebra [12] is the CΓ-algebra Hψ defined by Hψ = (TV#Γ)/I(x⊗ y − y ⊗ x− ψ(x, y) ; x, y ∈ V ), Actually, for any map m : Γ → C which is constant on any conjugation class, m · ψ is Γ-equivariant, and Hm·ψ is also called a symplectic reflection algebra.”
• Projective-injective modules, Serre functors and symmetric algebras (2005, unknown): “(This is the PBW-theorem [26], Theorem 1.”
• Microlocalization of rational Cherednik algebras (2007, background): “290 pp. [6] Etingof, Pavel and Ginzburg, Victor, Symplectic reflection algebras, Calogero-Moser space, and de- formed Harish-Chandra homomorphism, Invent.”
• On category O for cyclotomic rational Cherednik algebras (2011, background): “In [26] Etingof and Ginzburg introduced symplectic reflection algebras.”
• Geometric representations of graded and rational Cherednik algebras (2014, background): “Etingof and Ginzburg [18] introduced the graded Cherednik algebra Hgrν and rational Cherednik algebra Hratν which are the degenerations of the corresponding double Affine Hecke algebras.”