  We extend the work of Ash and Stevens [Ash-Stevens 97] on p-adic analytic
families of p-ordinary arithmetic cohomology classes for GL(N,Q) by introducing
and investigating the concept of p-adic rigidity of arithmetic Hecke
eigenclasses. An arithmetic eigenclass is said to be "rigid" if (modulo
twisting) it does not admit a nontrivial p-adic deformation containing a
Zariski dense set of arithmetic specializations. This paper develops tools for
explicit investigation into the structure of eigenvarieties for GL(N). We use
these tools to prove that known examples of non-sefldual cohomological
cuspforms for GL(3) are rigid. Moreover, we conjecture that for GL(3), rigidity
is equivalent to non-selfduality.
