Noncompact Semisimple Lie Algebras and Groups by Vladimir K. Dobrev

Author:Vladimir K. Dobrev
Language: eng
Format: epub, pdf
Publisher: De Gruyter
Published: 2016-03-15T00:00:00+00:00

where κ0 = π4 is introduced for convenience, dk is the normalized Haar measure on K. The representation T χ0 is continuous w.r.t. the topology defined by (6.98). It is complete as normed only w.r.t a Fréchet space topology which we could have introduced in line with [159, 620]. The completion of Cχ0 with respect to (6.98) shall be denoted by . The scalar product (6.98) is also G-invariant iff ck = irk, rk ∈ , k = 1, 2. Then the latter ERs form the principal series of unitary representations of G acting in [351].

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