  This paper presents a group-theoretical vector space model (VSM) that extends
the VSM with a group action on a vector space of the VSM. We use group and its
representation theory to represent a dynamic transformation of information
objects, in which each information object is represented by a vector in a
vector space of the VSM. Several groups and their matrix representations are
employed for representing different kinds of dynamic transformations of
information objects used in the VSM. We provide concrete examples of how a
dynamic transformation of information objects is performed and discuss
algebraic properties involving certain dynamic transformations of information
objects used in the VSM.
