Degenerate Principal Series Representations of GLn(C) and GLn(R)
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Let F be the field C or R. For 1≤k≤[n/2], 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. © 1999 Academic Press.
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