Conference abstracts

Session S08 - Lie Groups and Representations

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Chiral De Rham Complex Structure for Witt algebras

IME - USP, Brazil   -   andrezaidan@gmail.com

The Chiral de Rham complex in the case of a torus $\mathbb{T}^N$, is a tensor product of two vertex super algebras: $V^+_{Hyp}\otimes V_{\mathbb{Z}^N}$, one is the hyperbolic latice vertex algebra and the other is the euclidean latice vertex algebra. The space $M_{Hyp}(\gamma)\otimes V^k_{\mathbb{Z}^N}$ has a structure of a module for the Witt algebra, , where $M_{Hyp}(\gamma)$ is a module for the hyperbolic latice vertex algebra and $V^k_{\mathbb{Z}^N}$ is the subspace of fermionic degree $k$. These modules exhaust all exceptional generalized highest weight modules for this Lie algebra.