Dual Pairs inPin(p, q) and Howe Correspondences for the Spin Representation
✍ Scribed by M.J Slupinski
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 329 KB
- Volume
- 202
- Category
- Article
- ISSN
- 0021-8693
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✦ Synopsis
In this paper we obtain examples of dual pairs in the group Pin V m W by Ž . Ž . considering the inverse images of the subgroups O V m Id and Id m O W W V Ž . Ž . under the double covering map : Pin V m W ª O V m W . The main technical results are the definition of the group of determinant graded double covers of Ž . y1 Ž Ž . . O V and the fact that the map W ¬ O V m Id defines a homomorphism W Ž . 2 from the Witt group to this group when the ground field k satisfies k*r k* ( ޚ 2 and y1 is not a square in k. We also show that the spin representation of Ž . Pin V m W sets up Howe correspondences for each of these dual pairs when k s .ޒ ᮊ 1998 Academic Press