Mark Skandera: A conjectured combinatorial interpretation for induced sign
characters of the Hecke algebra
Abstract
Many combinatorial formulas for computations in the
symmetric group Sn
can be modified appropriately to describe computations in the Hecke
algebra Hn(q),
a deformation of
C[Sn].
Unfortunately, the known formulas for induced sign characters of
Sn
are not among these.
For induced sign characters of
Hn(q),
we conjecture formulas which specialize at
q=1
to formulas for induced sign characters of
Sn.
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.