Mod p decompositions of the loop spaces of compact symmetric spaces
  We give p-local homotopy decompositions of the loop spaces of compact, simply-connected symmetric spaces for quasi-regular primes. The factors are spheres, sphere bundles over spheres, and their loop spaces. As an application, upper bounds for the homotopy exponents are determined. 
Shizuo Kaji, Akihiro Ohsita and Stephen Theriault
math.AT