Stable decompositions of certain representations of the finite general   linear groups
  We prove that the irreducible decomposition of the permutation representation of GL(n,q) on GL(n,q)/GL(n-m,q) stabilizes for large n. We deduce, as a consequence, a representation stability theorem for finitely generated VIC-modules. 
Wee Liang Gan, John Watterlond
math.RT