  In this paper, we derive a relation of new kind between certain character
values of symmetric groups in terms of so-called maya diagrams. We also
investigate a relation between our result and Bernstein's creation operators
for Schur functions, and consider analogous relations for projective characters
of symmetric groups through creation operators for Schur $Q$-functions. We also
consider analogous relations for characters of Brauer algebras and walled
Brauer algebras.
