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Presented By: Geometry Seminar - Department of Mathematics

GEOMETRY: Hidden Sp(1)-symmetry and brane quantization on hyperKähler manifolds

Yu Tung Yau

In a joint work with Conan Leung, we found a natural but hidden Sp(1)-action on the space of L-valued forms on a hyperKähler manifold X intertwining a twistor family of Spinc-Dirac Laplacians of the space of L-valued (0, *)-forms for a fixed prequantum line bundle L over X, noting that L is holomorphic with respect to only one complex structure in the twistor family. In this talk, I will explain how this result establishes a geometric quantization of X via Gukov-Witten brane quantization and leads to a proposal of a mathematical definition of the morphism space between the canonical coisotropic A-brane on X and its conjugate brane.

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