A well studied (q,t)-analogue of symmetric functions are the
Macdonald polynomials. In this talk I will survey another (q,t)-analogue, where
q is a prime power from a finite field and t is an indeterminate. Analogues of facts
about the symmetric group S_n are given for GL_n(F_q), including
(1) counting factorizations of certain elements into reflections,
(2) combinatorial properties of appropriate (q,t)-binomial coefficients,
(3) Hilbert series for invariants on polynomial rings.
Some new conjectured explicit Hilbert series of rings of invariants are given.
This is joint work with Joel Lewis and Vic Reiner.