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Session 26. Physics and Differential Topology
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Symplectic analogues of the Dirac and the twistor operators and their solution spaces on \(\mathbb{R}^{2n}\) and \(2n\)-dimensional tori
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Marie Dostálová, Mathematical Institute of Charles University, Czech Republic
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The symplectic Dirac and the symplectic twistor operators are Spin-symplectic
analogues of the Dirac and the twistor operators in the (pseudo-)Riemannian
Spin geometry. In particular, for standard symplectic space \((\mathbb{R}^{2n},\omega)\) there is a
difference between the solution spaces of the symplectic twistor operator in the
case \(n = 1\) respectively \(n > 1\). The main technical tool used to determine these
solution spaces, is based on the metaplectic Howe duality.
On the examples of \(2n\)-dimensional tori we demonstrate the effect of dependence of the solution spaces of the symplectic Dirac and the symplectic twistor
operators on the choice of the metaplectic structure.
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