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Quantum multiplicative hypertoric varieties at a root of unity

Algebra & Discrete Mathematics

Speaker: Iordan Ganev, UT Austin
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Location: 2112 MSB
Start time: Mon, Feb 2 2015, 5:10PM

Hypertoric varieties are hyperkahler analogues of toric varieties related to symplectic resolutions, hyperplane arrangements, and geometric representation theory. We construct quantizations, depending on a parameter q, of multiplicative hypertoric varieties using an algebra of difference operators on affine space. Furthermore, when q is a root of unity, we show that the quantization acquires a large center and defines a matrix bundle (i.e. Azumaya algebra) over the multiplicative hypertoric variety.