We study the relative Donaldson-Thomas theory of A_n x P^1, where A_n is the surface resolution of a type A_n singularity. The action of divisor operators in the theory is expressed in terms of operators of the affine algebra \hat{gl}(n+1) on Fock space. Assuming a nondegeneracy conjecture, this gives a complete solution for the theory. The results complete the comparison of this theory with the Gromov-Witten theory of A_n x P^1 and the quantum cohomology of the Hilbert scheme of points on A_n.Comment: 30 pages, 2 figures; minor change

Topics:
Mathematics - Algebraic Geometry, Mathematics - Representation Theory

Year: 2008

OAI identifier:
oai:arXiv.org:0802.2739

Provided by:
arXiv.org e-Print Archive

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http://arxiv.org/abs/0802.2739

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