Abstract: A classical combinatorial result (originally due to Denes) is that there are precisely n^(n - 2) factorizations of a long cycle in the symmetric group S_n as a product of n - 1 transpositions. This result has subsequently been generalized in many directions, e.g., to factorizations of Coxeter elements in a (real or complex) reflection group. In this talk, I'll discuss joint work with Vic Reiner and Dennis Stanton on a q-analogue, replacing the symmetric group with the general linear group GL_n(F_q), the long cycle with a Singer cycle, and transpositions with reflections. Using the (ordinary) representation theory of GL_n, we've shown that the number of shortest such factorizations is (q^n - 1)^(n - 1). I'll discuss this result, as well as some extensions and open questions.