A supercharacter table decomposition via power-sum symmetric functions

Details A supercharacter table decomposition via power-sum symmetric functions A supercharacter table decomposition via power-sum symmetric functions

2011-12-21

arxiv.org/abs/1112.4901v3

Mathematics

Representation Theory

(minor modification with references) 9 pages, preliminary version

Scientific paper

We give an $AB$-factorization of the supercharacter table of the group of $n\times n$ unipotent upper triangular matrices over $\FF_q$, where $A$ is a lower-triangular matrix with entries in $\ZZ[q]$ and $B$ is a unipotent upper-triangular matrix with entries in $\ZZ[q^{-1}]$. To this end we introduce a $q$ deformation of a new power-sum basis of the Hopf algebra of symmetric functions in noncommutative variables. The factorization is obtain from the transition matrices between the supercharacter basis, the $q$-power-sum basis and the superclass basis. This is similar to the decomposition of the character table of the symmetric group $S_n$ given by the transition matrices between Schur functions, monomials and power-sums. We deduce some combinatorial results associated to this decomposition. In particular we compute the determinant of the supercharacter table.

Affiliated with

Also associated with

No associations

Rating

A supercharacter table decomposition via power-sum symmetric functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A supercharacter table decomposition via power-sum symmetric functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A supercharacter table decomposition via power-sum symmetric functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-190793