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@article{Bellamy:2018:10.1007/s11005-017-1002-7,
author = {Bellamy, G and Schedler, TJ},
doi = {10.1007/s11005-017-1002-7},
journal = {Letters in Mathematical Physics},
pages = {679--698},
title = {Filtrations on Springer fiber cohomology and Kostka polynomials},
url = {http://dx.doi.org/10.1007/s11005-017-1002-7},
volume = {108},
year = {2018}
}

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TY  - JOUR
AB  - We prove a conjecture which expresses the bigraded Poisson-de Rham homology of the nilpotent cone of a semisimple Lie algebra in terms of the generalized (one-variable) Kostka polynomials, via a formula suggested by Lusztig. This allows us to construct a canonical family of filtrations on the flag variety cohomology, and hence on irreducible representations of the Weyl group, whose Hilbert series are given by the generalized Kostka polynomials. We deduce consequences for the cohomology of all Springer fibers. In particular, this computes the grading on the zeroth Poisson homology of all classical finite W-algebras, as well as the filtration on the zeroth Hochschild homology of all quantum finite W-algebras, and we generalize to all homology degrees. As a consequence, we deduce a conjecture of Proudfoot on symplectic duality, relating in type A the Poisson homology of Slodowy slices to the intersection cohomology of nilpotent orbit closures. In the last section, we give an analogue of our main theorem in the setting of mirabolic D-modules.
AU  - Bellamy,G
AU  - Schedler,TJ
DO  - 10.1007/s11005-017-1002-7
EP  - 698
PY  - 2018///
SN  - 0377-9017
SP  - 679
TI  - Filtrations on Springer fiber cohomology and Kostka polynomials
T2  - Letters in Mathematical Physics
UR  - http://dx.doi.org/10.1007/s11005-017-1002-7
UR  - http://hdl.handle.net/10044/1/51210
VL  - 108
ER  -

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