Chinese Acad Sci, Inst High Energy Phys, Beijing 100049, Peoples R China
; Chinese Acad Sci, Inst Theoret Phys, Beijing 100080, Peoples R China
; Beijing Inst Technol, Dept Phys, Beijing 100081, Peoples R China
; Capital Normal Univ, Dept Math, Beijing 100037, Peoples R China
; Tsing Hua Univ, Dept Phys, Beijing 100084, Peoples R China
; Beijing Normal Univ, Dept Phys, Beijing 100875, Peoples R China
Between Snyder's quantized space-time model in de Sitter space of momenta and the dS special relativity on dS-spacetime of radius R with Beltrami coordinates, there is a one-to-one dual correspondence supported by a minimum uncertainty-like argument. Together with the Planck length l(P), R similar or equal to (3/ Lambda)(1/2) should be a fundamental constant. They lead to a dimensionless constant g similar or equal to l(p) R-1 = (Ghc(-3) Lambda / 3)(1/2) similar to 10(-61). These indicate that physics at these two scales should be dual to each other and there is in- between gravity of local dS- invariance characterized by g. A simple model of dS-gravity with a gauge-like action on umbilical manifolds may show these characteristics. It can pass the observation tests and support the duality.