Degenerate Principal Series Representations of GLn(C) and GLn(R)

✍ Scribed by Roger Howe; Soo Teck Lee

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 499 KB
• Volume: 166
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1999.3427

✦ Synopsis

Let F be the field C or R. For 1 k [nÂ2], let P k be the maximal parabolic subgroup of GL n (F) with its Levi factor isomorphic to GL n&k (F)_GL k (F ). In this paper, we explicitly calculate the action of the enveloping algebra of gl n (F) on the degenerate principal series representations induced from characters of P k . We address composition series, K-types and unitarity.