Rational Cherednik algebras and Hilbert schemes II: representations and sheaves
| dc.creator | Gordon, I. | |
| dc.creator | Stafford, J. T. | |
| dc.date | 2004-10-12 | |
| dc.date.accessioned | 2026-07-07T05:13:12Z | |
| dc.date.available | 2026-07-07T05:13:12Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/math/0410293 | |
| dc.identifier | http://arxiv.org/abs/math/0410293 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72862 | |
| dc.subject | Representation Theory | |
| dc.subject | Rings and Algebras | |
| dc.title | Rational Cherednik algebras and Hilbert schemes II: representations and sheaves | |
| dc.type | text |