Abstract: 

 Abstract: For each $ \lambda \in \R $ there is a Hilbert space of entire functions $ \mathcal{F}_\lambda(\C^{2n}) $ known as twisted Fock space. We show that within this space there is an algebra $ \mathcal{A}_\lambda(\C^{2n}) $ which is isometrically isomorphic to $ B(L^2(\R^n)).$ The map $ U $ defined by $ UF(z,w) =F(-iz,-iw) $ is a unitary operator on $ \mathcal{F}_\lambda(\C^{2n}) .$ We show that for any $ \varphi \in \mathcal{A}_\lambda(\C^{2n}),$ the function $ U\varphi $ can never be in $ \mathcal{A}_\lambda(\C^{2n})$ unless $ \varphi $ is a constant. This has an interpretation as an uncertainty principle for a class of operators of convolution type on the Fock space  $\mathcal{F}_\lambda(\C^{2n}).$ 

 This talk is based on my recent joint work with Rahul Garg.