Cherednik algebras and Hilbert schemes in characteristic $p$
نویسندگان
چکیده
منابع مشابه
Rational Cherednik Algebras and Hilbert Schemes Ii: Representations and Sheaves
Let Hc be the rational Cherednik algebra of type An−1 with spherical subalgebra Uc = eHce. Then Uc is filtered by order of differential operators with associated graded ring grUc = C[h ⊕ h∗]W , where W is the n-th symmetric group. Using the Z-algebra construction from [GS] it is also possible to associate to a filtered Hcor Uc-module M a coherent sheaf Φ̂(M) on the Hilbert scheme Hilb(n). Using ...
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Lowest-weight representations of Cherednik algebras H~,c have been studied in both characteristic 0 and positive characteristic. However, the case of positive characteristic has been studied less, because of a lack of general tools. In positive characteristic the lowest-weight representation Lc(τ) of the Cherednik algebra is finite-dimensional. The representation theory of complex reflection gr...
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We construct projective moduli spaces for torsion-free sheaves on noncommutative projective planes. These moduli spaces vary smoothly in the parameters describing the noncommutative plane and have good properties analogous to those of moduli spaces of sheaves over the usual (commutative) projective plane P. The generic noncommutative plane corresponds to the Sklyanin algebra S = Skl(E,σ) constr...
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We construct a functor from the category of modules over the trigonometric (resp. rational) Cherednik algebra of type gll to the category of integrable modules of level l over a Yangian for the loop algebra sln (resp. over a subalgebra of this Yangian called the Yangian deformed double loop algebra) and we establish that it is an equivalence of categories if l + 2 < n.
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We survey a number of results about rational Cherednik algebra representation theory and its connection to symplectic singularities and their resolutions. Mathematics Subject Classification (2000). Primary 16G, 17B; Secondary 20C, 53D.
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ژورنال
عنوان ژورنال: Representation Theory of the American Mathematical Society
سال: 2006
ISSN: 1088-4165
DOI: 10.1090/s1088-4165-06-00309-8