Eisenstein series on weakly spherical homogeneous spaces of \(GL(n)\)
Let \(G\) be a connection reductive algebraic group and let \(P\) be a proper parabolic subgroup. A homogeneous space \(X=G/H\) is called \(P\)-spherical if there exists a Zariski-open \(P\)-orbit in \(X\). It is also called weakly spherical. The purpose of this paper is to construct generalized Eisenstein series attached to the weakly spherical homogeneous space when \(G\) is a product of several general linear groups and \(P\) is its (not necessarily maximal) parabolic subgroup. The author of this paper constructed generalized Eisenstein series as complex multivariate functions and proved that they are meromorphic with respect to the complex numbers under suitable conditions on \(P\) and \(H\). Then he proves that Eisenstein series satisfy functional equations and give their explicit forms.
scientific article; zbMATH DE number 1185532
scientific article