Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rational Cherednik algebras and Hilbert schemes II: representations and
  sheaves   Let H_c be the rational Cherednik algebra of type A_{n-1} with spherical
subalgebra U_c=eH_ce. Then U_c is filtered by order of differential operators
with associated graded ring gr U_c=C[h + h*]^W, where W is the n-th symmetric
group. Using the Z-algebra construction from our earlier paper
(math.RA/0407516) it is also possible to associate to a filtered H_c- or
U_c-module M a coherent sheaf on the Hilbert scheme Hilb(n).
  Using this technique, we study the representation theory of U_c and H_c, and
relate it to Hilb(n) and to the resolution of singularities from Hilb(n) to
h+h*/W. For example, we prove:
  (1) If c=1/n, so that L_c(triv) is the unique one-dimensional simple
H_c-module, then L_c(triv) corresponds to the structure sheaf of the punctual
Hilbert scheme.
  (2) If c=1/n+k (for k some natural number) then, under a canonical filtration
on the finite dimensional module L_c(triv), gr eL_{c}(triv) has a natural
bigraded structure which coincides with that on the global sections of certain
ample line bundles on the punctual Hilbert scheme; this confirms conjectures of
Berest, Etingof and Ginzburg, and relates representations of H_c and U_c with
Haiman's combinatorial work on the Hilbert scheme.
  (3) Under mild restrictions on c, the characteristic cycle of the standard
H_c-modules are described in terms of certain irreducible subvarieties of the
Hilbert scheme (appearing originally in work of Grojnowski) with multiplicities
given by Kostka numbers.

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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: funct-an