Decomposition of gamma matrices of local zeta functions associated with homogeneous cones
Copyright policy )Decomposition of gamma matrices of local zeta functions associated with homogeneous cones
The paper under review deals with coefficient matrices of functional equations of zeta functions associated with homogeneous cones studied by the author in a previous paper [Tohoku Math. J. (2) 72, No. 3, 349--378 (2020; Zbl 1457.11126)]. More precisely, it is shown that the associated gamma matrices can always be decomposed into a product of diagonal matrices each of whom is in a single variable and of orthogonal matrices. Furthermore, the author shows that the associated zeta functions have completions for a certain class of homogeneous cones.
Nilpotent and solvable Lie groups, zeta functions, functional equations, Prehomogeneous vector spaces, prehomogeneous vector spaces, Other Dirichlet series and zeta functions, homogeneous cones
Nilpotent and solvable Lie groups, zeta functions, functional equations, Prehomogeneous vector spaces, prehomogeneous vector spaces, Other Dirichlet series and zeta functions, homogeneous cones
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