Complex Analysis and Operator Theory

, Volume 8, Issue 2, pp 513–528 | Cite as

Symplectic Twistor Operator on \(\mathbb R ^{2n}\) and the Segal–Shale–Weil Representation

Article

Abstract

The aim of our article is the study of solution space of the symplectic twistor operator \(T_s\) in symplectic spin geometry on standard symplectic space \((\mathbb R ^{2n},\omega )\), which is the symplectic analogue of the twistor operator in (pseudo) Riemannian spin geometry. In particular, we observe a substantial difference between the case \(n=1\) of real dimension \(2\) and the case of \(\mathbb R ^{2n}, n>1\). For \(n>1\), the solution space of \(T_s\) is isomorphic to the Segal–Shale–Weil representation.

Keywords

Symplectic twistor operator Symplectic Dirac operator  Metaplectic Howe duality 

Mathematics Subject Classification

53C27 53D05 81R25 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Mathematical Institute of Charles UniversityPraha 8Czech Republic

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