2 4 Ja n 20 02 Euler - Poincaré functions Anton Deitmar
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چکیده
Euler-Poincaré functions and pseudo-coefficients are important tools in harmonic analysis since they help to single out a given representation in direct integrals or sums. Given a real reductive groupG that admits a compact Cartan subgroup, these functions can be attached to a given finite dimensional representation τ of a maximal compact subgroup K. In [10] a construction was given in the case when τ extends to the bigger group G. In this paper we give a new construction for an arbitrary representation τ . Instead, we put a condition on the group G, namely, that it acts orientation preservingly on the symmetric space G/K. This condition is satisfied if G is connected or if it respects a complex structure on G/K. For connected G the existence of Euler-Poincaré functions is known [4], but this is not always sufficient for applications since Levi components are not in general connected, even if
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تاریخ انتشار 2002