A Survey of $q$-Whittaker polynomials

Exploiting the fact that the $q$-Whittaker polynomials arise as a specialization of the (modified) Macdonald polynomials, we derive some of their basic properties, and explore interesting identities that they satisfy. We also show how they arise as graded Frobenius characteristics of ${\mathrm{\S }}_n$-modules, and give a combinatorial approach to associated Pieri formulas.