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Quantum algebras and symplectic reflection algebras for wreath products

Quantum algebras and symplectic reflection algebras for wreath products,10.1090/S1088-4165-10-00366-3,Representation Theory of The American Mathematic

Quantum algebras and symplectic reflection algebras for wreath products   (Citations: 3)
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To a nite subgroup of SL2(C), we associate a new family of quantum algebras which are related to symplectic reection algebras for wreath products Sl o via a functor of Schur-Weyl type. We explain that they are deformations of matrix algebras over rank-one symplectic reection algebras for and construct for them a PBW basis. When is a cyclic group, we are able to give more information about their structure and to relate them to Yangians.
Journal: Representation Theory of The American Mathematical Society , vol. 14, no. 04, pp. 148-200, 2010
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    • ...This is motivated by the recent work [Gu3] in which...
    • ...The proof of proposition 4.4 in [MRY] works also for b sln(B) and it is possible to deduce from it proposition 5.3. See [Gu3] for more details...
    • ...algebras and the G-DDCA of [Gu1, Gu2, Gu3] are also deformations of the enveloping algebra of gln(A1 ⋊ ) when G is a finite subgroup of SL2(C)...
    • ...Moreover, as is explained in [Gu3], Ht,c() depends actually only on the t parameter, that is, Ht,c() ∼= Ht,c=0() , but this is not true for Ht,c() . An explicit isomorphism...
    • ...This definition applies also to the -deformed double curren t algebras Dnλ,b() of [Gu3]...
    • ...One justification for it is that the Schur-Weyl functor studied in [Gu1, Gu3] sends modules in the category O of a rational Cherednik algebra for ×l ⋊ Sl to a module in O Dnλ,b() �...

    Nicolas Guayet al. Double affine Lie algebras and finite groups

    • ...The map Θ Quiver introduced in this paper turns out to be useful in the theory of deformed double current algebras developed by N. Guay [Gu1,Gu2,Gu3]...

    Pavel Etingofet al. Harish–Chandra homomorphisms and symplectic reflection algebras for wr...

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