# Is there a Murnaghan-Nakayama Rule for GL(n,q)?

The Murnaghan-Nakayama rule for S_n is a combinatorial rule to compute the irreducible characters of the symmetric group. Is there a q-analogue of this rule for GL(n,q) to compute the irreducible characters? For example, exhibiting that the value of the unipotent characters of GL(n,q) on a unipotent class is given by the cocharge Kostka-Foulkes polynomials, and showing other special cases.

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