Electronic Journal of Combinatorics
Gelfand-Graev characters and their degenerate counter parts have an important role in there presentation 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
Thiem, N., & Vinroot, C. R. (2009). Gelfand–Graev characters of the finite unitary groups. the electronic journal of combinatorics, 16(1), R146.