Digital Commons Network^™

Laguerre Functions Associated To Euclidean Jordan Algebras, Michael Aristidou

LSU Doctoral Dissertations

Certain differential recursion relations for the Laguerre functions, defined on a symmetric cone Ω, can be derived from the representations of a specific Lie algebra on L²(Ω,dμ_v). This Lie algebra is the corresponding Lie algebra of the Lie group G that acts on the tube domain T(Ω)=Ω+iV, where V is the associated Euclidean Jordan algebra of Ω. The representations involved are the highest weight representations of G on L²(Ω,dμ_v). To obtain these representations, we start from the highest weight representations of G on H_v(T(Ω)), the Hilbert space of holomorphic functions …