On $C$-bases, partition pairs and filtrations for induced or restricted Specht modules
  We obtain alternative explicit Specht filtrations for the induced and the
restricted Specht modules in the Hecke algebra of the symmetric group (defined
over the ring $A=\mathbb Z[q^{1/2},q^{-1/2}]$ where $q$ is an indeterminate)
using $C$-bases for these modules. Moreover, we provide a link between a
certain $C$-basis for the induced Specht module and the notion of pairs of
partitions.
