Cuspidal Representations Associated to (GL(n), O(n)) over Finite Fields andp-Adic Fields
✍ Scribed by Jeffrey Hakim; Zhengyu Mao
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 137 KB
- Volume
- 213
- Category
- Article
- ISSN
- 0021-8693
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✦ Synopsis
When r is an irreducible cuspical representation of G s GL n, q and H is an orthogonal group associated to a symmetric matrix in G then the space of H-fixed vectors for r is shown to have dimension at most one. Such a representation r Ž . induces an irreducible supercuspidal representation of G s GL n, E , where E is a p-adic field whose residue field has order q. The space of those linear forms on the space of which are invariant under an orthogonal group is computed. For the corresponding group of orthogonal similitudes, it is shown that the dimension of the space of invariant linear forms is always at most one. ᮊ 1999 Academic Press H * The authors gratefully acknowledge H. Jacquet for suggesting this research. We also mention that the referee has pointed out that some of our proofs might be simplified w x somewhat by appealing to the results of 14 . We have chosen, however, to leave the paper in its present form so that it is more accessible to experts in various fields.