  We use vertex operators to compute irreducible characters of the
Iwahori-Hecke algebra of type $A$. Two general formulas are given for the
irreducible characters in terms of those of the symmetric groups or the
Iwahori-Hecke algebras in lower degrees. Explicit formulas are derived for the
irreducible characters labeled by hooks and two-row partitions. Using duality,
we also formulate a determinant type Murnaghan-Nakayama formula and give
another proof of Ram's combinatorial Murnaghan-Nakayama formula. As
applications, we study super-characters of the Iwahori-Hecke algebra as well as
the bitrace of the regular representation and provide a simple proof of the
Halverson-Luduc-Ram formula.
