1 3 O ct 2 01 3 Representations of rational Cherednik algebras of G ( m , r , n ) in positive characteristic Sheela Devadas Steven
نویسندگان
چکیده
We study lowest-weight irreducible representations of rational Cherednik algebras attached to the complex reflection groups G(m, r, n) in characteristic p. Our approach is mostly from the perspective of commutative algebra. By studying the kernel of the contravariant bilinear form on Verma modules, we obtain formulas for Hilbert series of irreducible representations in a number of cases, and present conjectures in other cases. We observe that the form of the Hilbert series of the irreducible representations and the generators of the kernel tend to be determined by the value of n modulo p, and are related to special classes of subspace arrangements. Perhaps the most novel (conjectural) discovery from the commutative algebra perspective is that the generators of the kernel can be given the structure of a “matrix regular sequence” in some instances, which we prove in some small cases.
منابع مشابه
Lowest-weight representations of Cherednik algebras in positive characteristic
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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