Determinantal formulas with major indices

Thomas McConville, Kennesaw State University
Donald Robertson, The University of Manchester
Clifford Smyth, The University of North Carolina at Greensboro


We give an elementary proof of a major index determinant formula discovered by Krattenthaler and first proved by Thibon using noncommutative symmetric functions. We do so by proving a factorization of an element in the group ring of the symmetric group. By applying similar methods to the groups of signed permutations and colored permutations, we prove determinantal formulas in these groups as conjectured by Krattenthaler.