Verdiyev, YA2024-06-122024-06-1219970305-4470https://doi.org/10.1088/0305-4470/30/11/033https://hdl.handle.net/20.500.14551/25760Plane waves on symmetric spaces (SS) X = SO(p,q)/SO(p) circle times SO(q) of rank p, p less than or equal to q, are constructed by realization of the irreducible representations (principal series) of the group SO(p,q) in the space of infinitely differentiable homogeneous vector functions F(y(i)) on cones [y(i), y(i)] = 0,y(i) epsilon Y-i, with values in the representation space of the stability subgroups SO(p - i, q - i), i = 1,..., p. We define the cones Y-i = Lim X(alpha(i),...,alpha(p)), alpha(i) --> infinity, corresponding to the SS X related with Cartan involutive automorphism sigma(g) = Igl, g epsilon SO(p,q), where I = diag(1,...,1,-1,...,-1) is the metric tensor of the pseudo-Euclidean space R-p.4 Calculating Harish-Chandra c-functions the orthogonality, completeness conditions and addition theorems for plane waves are derived. The integrable n-body quantum systems related to groups SO(p, q) are considered. The explicit expressions for the Green functions in the case SS X of rank p = 1 and the integral representation in the general case are given.en10.1088/0305-4470/30/11/033info:eu-repo/semantics/closedAccess[No Keywords]Article301140894107Q1WOS:A1997XE208000332-s2.0-0038867291N/A