In this paper it is proved that the principal series of representations of F = Z_2* • • • *Z_2 may be analytically continued to give uniformly bounded representations on the same Hilbert space, and that these representations are irreducible. Further, the reducibility of the restrictions to Γ ⊂ SL(2,Q_p) of the irreducible unitary representations of SL(2,Q_p) is examined.
Irreducibility of the analytic continuation of the principal series of a free group
MANTERO, ANNA MARIA;ZAPPA, ANNA
1987-01-01
Abstract
In this paper it is proved that the principal series of representations of F = Z_2* • • • *Z_2 may be analytically continued to give uniformly bounded representations on the same Hilbert space, and that these representations are irreducible. Further, the reducibility of the restrictions to Γ ⊂ SL(2,Q_p) of the irreducible unitary representations of SL(2,Q_p) is examined.
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