  Let T be an involution of the finite dimensional complex reductive Lie
algebra g and g=k+p be the associated Cartan decomposition. Denote by K the
adjoint group of k.
  The K-module p is the union of the subsets p^{(m)}={x | dim K.x =m}, indexed
by integers m, and the K-sheets of (g,T) are the irreducible components of the
p^{(m)}. The sheets can be, in turn, written as a union of so-called Jordan
K-classes.
  We introduce conditions in order to describe the sheets and Jordan K-classes
in terms of Slodowy slices. When g is of classical type, the K-sheets are shown
to be smooth; if g=gl_N a complete description of sheets and Jordan K-classes
is then obtained.
