Gelfand-Graev Characters of the Finite Unitary Groups

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.