  Gelfand-Graev characters and their degenerate counterparts have an important
role in the representation theory of finite groups of Lie type. Using a
characteristic map to translate the character theory of the finite unitary
groups into the language of symmetric functions, we study degenerate
Gelfand-Graev characters of the finite unitary group from a combinatorial point
of view. In particular, we give the values of Gelfand-Graev characters at
arbitrary elements, recover the decomposition multiplicities of degenerate
Gelfand-Graev characters in terms of tableau combinatorics, and conclude with
some multiplicity consequences.
