A SUPERCHARACTER TABLE DECOMPOSITION VIA POWER-SUM SYMMETRIC FUNCTIONS Journal Article uri icon

Overview

abstract

  • We give an LU-decomposition of the supercharacter table of the group of n × n unipotent upper triangular matrices over �q, into a lower-triangular matrix with entries in ℤ[q] and an upper-triangular matrix with entries in ℤ[q-1]. To this end, we introduce a q deformation of a new power-sum basis of the Hopf algebra of symmetric functions in noncommuting variables. The decomposition is obtained 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 Sngiven 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.

publication date

  • June 1, 2013

has restriction

  • green

Date in CU Experts

  • January 18, 2017 3:20 AM

Full Author List

  • BERGERON N; THIEM N

author count

  • 2

Other Profiles

International Standard Serial Number (ISSN)

  • 0218-1967

Electronic International Standard Serial Number (EISSN)

  • 1793-6500

Additional Document Info

start page

  • 763

end page

  • 778

volume

  • 23

issue

  • 04