On the invariant scalar products and the UIR of SO (n,1)
Takayoshi Maekawa · Journal of Mathematical Physics · 1980
A quantity, which is invariant under the transformation of h∈SO (n,1), is found in a form of the series expansion in terms of the D matrix elements of SO (n) and an invariant scalar product, which is needed for the complementary series of the unitary irreducible representation of SO (n,1), is introduced in the Hermitian form by using the invariant quantity. The action of the intertwining operator defined through the Hermitian scalar product to the bases of Hc, on which the complementary series of the UIR of SO (n,1) are realized, is found.