Boundary value maps, Szegö maps and intertwining operators

Author:
L. Barchini

Journal:
Trans. Amer. Math. Soc. **349** (1997), 1877-1900

MSC (1991):
Primary 22C05, 22E45, 22E46

DOI:
https://doi.org/10.1090/S0002-9947-97-01834-5

MathSciNet review:
1401761

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider one series of unitarizable representations, the cohomological induced modules with dominant regular infinitesimal character. The minimal -type of determines a homogeneous vector bundle . The derived functor modules can be realized on the solution space of a first order differential operator on . Barchini, Knapp and Zierau gave an explicit integral map from the derived functor module, realized in the Langlands classification, into the space of smooth sections of the vector bundle . In this paper we study the asymptotic behavior of elements in the image of . We obtain a factorization of the standard intertwining opeartors into the composition of the Szegö map and a passage to boundary values.

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Additional Information

**L. Barchini**

Affiliation:
Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122

Address at time of publication:
Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078

Email:
leticiz@math.okstate.edu

DOI:
https://doi.org/10.1090/S0002-9947-97-01834-5

Received by editor(s):
February 17, 1995

Received by editor(s) in revised form:
October 9, 1995

Article copyright:
© Copyright 1997
American Mathematical Society