Many combinatorial formulas for computations in the symmetric group S_n can be modified appropriately to describe computations in the Hecke algebra H_n(q), a deformation of C[S_n]. Unfortunately, the known formulas for induced sign characters of S_n are not among these. For induced sign characters of H_n(q), we conjecture formulas which specialize at q=1 to formulas for induced sign characters of S_n. We will discuss evidence in favor of the conjecture, and relations to the chromatic quasi-symmetric functions of Shareshian and Wachs.

This is joint work with Brittany Shelton of Lehigh University.