Baby Verma Modules for Rational Cherednik Algebras

By I. Gordon. 2002

126 citations recorded by the source corpus.

This paper introduces baby Verma modules for symplectic reflection algebras of complex reflection groups at parameter t = 0 (the so‐called rational Cherednik algebras at parameter t = 0, and presents their most basic properties. Baby Verma modules are then used to answer several problems posed by Etingof and Ginzburg, and to give an elementary proof of a theorem of Finkelberg and Ginzburg. 2000 Mathematics Subject Classification 16Rxx, 16S38, 05E10.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/74fea3b1582b873037e123c1e118c76210c293f4

How researchers see this paper

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In Geometry and Topology

1. I. Gordon
2. V. Ginzburg
3. Stephen Griffeth
4. J. T. Stafford
5. Pavel Etingof
6. I. Losev
7. Y. Berest
8. D. Kaledin

In Mathematical Physics

1. I. Gordon
2. V. Ginzburg
3. Stephen Griffeth
4. Pavel Etingof
5. J. T. Stafford
6. I. Losev
7. Y. Berest
8. D. Kaledin

In Statistical and Nonlinear Physics

1. J. T. Stafford
2. I. Gordon
3. V. Ginzburg
4. Pavel Etingof
5. Stephen Griffeth
6. Y. Berest
7. D. Kaledin
8. G. Bellamy

Citations in the corpus

• Orthogonal functions generalizing Jack polynomials (2007, background): “ indexed by the conjugacy classes of reflections in W. The representations of the rational Cherednik algebra are closely connected with many interesting problems. For instance, it was proved by Gordon [8] that when W is a Coxeter group and the parameters for H are chosen appropriately, the irreducibl”
• Rational Cherednik algebras and Hilbert schemes (2004, methodology): “[ BEG2 , Theorem 1.2] Uc±1-mod does have such modules and so there is no equivalence between Uc and Uc±1.”
• Poisson deformations of symplectic quotient singularities (2002, result): “ctor, by symplectic automorphisms. For types An, Bn, Cn the quotient V/Gis known to admit a crepant resolution of singularities (of Hilbert scheme type, see e.g. [Ku]). Using the results of I. Gordon [Go], we resolve the existence question for other Dynkin graphs to the negative: Theorem 1.1. For a ”
• Cherednik algebras and differential operators on quasi-invariants (2001, methodology): “) denote a pair of n×n-matrices in the conjugacy class corresponding to the fixed point in Mn labelled by the Young diagram Y(τ) (for a direct construction of this point in terms of the Sn-module τsee [Go], and [EG, Conjecture 17.14]). Now, using formula [Wi, (6.14)] for Schur functions (and formula ”
• LECTURES ON NAKAJIMA'S QUIVER VARIETIES (2009, background): “mbedding Γ ⊂ Sp(V). One can show that, among all irreducible finite Weyl groups Γ, only those of types A,B,and C, have the property that the orbifold (h×h∗)/Γ admits a symplectic resolution, see [GK], [Go]. In type A, we have Γ = Sn, the Symmetric group acting diagonally on Cn×Cn(two copies of the pe”