Juan Alfredo Tirao Dumont, Argentine mathematician (Cordoba 03 February 1942 – Introduced the notion of a presequence of matrix orthogonal polynomials to mean a sequence {F_n} of matrix orthogonal functions (2015) With B. Cox & V. Futorny showed that the family of Jacobi polynomials are orthogonal (2013) With P.M. Román obtained an inversion formula for the spherical transform by using the Fourier inversion formula in a locally compact group (2012) With F.A. Grunbaum introduced D(w) algebra of differential operators associated to a weight matrix (2011) Determinated the image of the Lepowsky homomorphism for the classic groups of rank one and the image of Ktype invariants ring in universal enveloping algebra of all Lie semisimple groups of rank one (2008) With F.A. Grunbaum & I. Pacharoni obtained explicit formulae in terms of definite integrals of all matrix entries of any power of matrix With F.A. Grunbaum & I. Pacharoni presented new families of Jacobi type matrix valued orthogonal polynomials (20035) With F.A. Grunbaum & I. Pacharoni defined the notion of a classical pair consisting of a matrix valued weight function and a second order symmetric differential operator (2003) Introduced the matrix valued hypergeometric function and established its properties in The matrix valued hypergeometric equation. Proceed. Nat. Acad. Sciences 100 (14):813841, 2003 With N. Andruskiewitsch introduced the notion of spherical representation of rank one of a complex reductive algebraic group Proposed spherical functions for homogeneous holomorphic vector bundles Formulated and proved necessary and sufficient conditions for the existence of a complex structure on a homogeneous vector bundle Obtained a characterization of the image of the classifying ring of Lie groups of rank one With N. Andruskiewitsch. A restriction theorem for modules having a spherical submodule. Trans. Amer. Mathem. Soc. 331(2), 1992 A restriction theorem for semisimple Lie groups of rank one. Trans. Amer. Mathem. Soc. (1983) (Tirao restriction theorem)

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