Can I read Zeroth Poisson homology of symmetric powers of isolated quasihomogeneous surface singularities on EtoBox?

Zeroth Poisson homology of symmetric powers of isolated quasihomogeneous surface singularities by Pavel Etingof; Travis Schedler is a Mathematics article available to read on EtoBox.

What is Zeroth Poisson homology of symmetric powers of isolated quasihomogeneous surface singularities about?

Let X H C 3 be a surface with an isolated singularity at the origin, given by the equation Qðx; y; zÞ 1⁄4 0, where Q is a weighted-homogeneous polynomial. In particular, this includes the Kleinian surfaces X 1⁄4 C 2 =G for G < SL 2 ðCÞ finite. Let Y :1⁄4 S n X be the n-th symmetric power of X . We compute the zeroth Poisson homology HP 0 ðO Y Þ, as a graded vector space with respect to the weight grading, where O Y is the ring of polynomial functions on Y . In the Kleinian case, this confirms a conjecture of Alev, that Þ, where Weyl 2n is the Weyl algebra on 2n generators. That is, the Brylinski spectral sequence degenerates in degree zero in this case. In the elliptic case, this yields the zeroth Hochschild homology of symmetric powers of the elliptic algebras with three generators modulo their center, A g , for all but countably many parameters g in the elliptic curve. As a consequence, we deduce a bound on the number of irreducible finitedimensional representations of all quantizations of Y . This includes the noncommutative spherical symplectic reflection algebras associated to G n z S n .

Who reads Zeroth Poisson homology of symmetric powers of isolated quasihomogeneous surface singularities?

Author

Pavel Etingof; Travis Schedler

Publisher

Walter de Gruyter GmbH

Published

2012

Field

Mathematics (Physical Sciences)