Dual Pairs in the Pin-Group and Duality for the Corresponding Spinorial Representation

@article{Guerin2020DualPI,
  title={Dual Pairs in the Pin-Group and Duality for the Corresponding Spinorial Representation},
  author={Cl'ement Gu'erin and Gang Liu and Allan Merino},
  journal={Algebras and Representation Theory},
  year={2020},
  volume={24},
  pages={1625-1640}
}
In this paper, we give a complete picture of Howe correspondence for the setting ( O ( E , b ), P i n ( E , b ),π), where O ( E , b ) is a real orthogonal group, P i n ( E , b ) is the two-fold Pin-covering of O ( E , b ), and π is the spinorial representation of P i n ( E , b ). More precisely, for a dual pair ( G , G ′ ) $(G, G^{\prime })$ in O ( E , b ), we determine explicitly the nature of its preimages ( G ~ , G ′ ~ ) $(\tilde {G}, \tilde {G^{\prime }})$ in P i n ( E , b ), and prove that… 
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