We classify the domains of holomorphy of all Harish-Chandra modules of
irreducible unitary representations of simple non-compact Lie groups.Comment: revised version, to appear in Invent. math., 14 page
We prove that the bicrossed product of two groups is a quotient of the
pushout of two semidirect products. A matched pair of groups (H,G,α,β) is deformed using a combinatorial datum (σ,v,r) consisting of
an automorphism σ of H, a permutation v of the set G and a
transition map r:G→H in order to obtain a new matched pair (H,(G,∗),α′,β′) such that there exist an σ-invariant
isomorphism of groups Hα​⋈β​G≅Hα′​⋈β′​(G,∗). Moreover, if we fix the group H and the automorphism
\sigma \in \Aut(H) then any σ-invariant isomorphism Hα​⋈β​G≅Hα′​⋈β′​G′ between two
arbitrary bicrossed product of groups is obtained in a unique way by the above
deformation method. As applications two Schreier type classification theorems
for bicrossed product of groups are given.Comment: 21 pages, final version to appear in Central European J. Mat