A SUPERCHARACTER TABLE DECOMPOSITION VIA POWER-SUM SYMMETRIC FUNCTIONS

作者：Bergeron Nantel^*; Thiem Nathaniel

来源：International Journal of Algebra and Computation, 2013, 23(4): 763-778.

DOI：10.1142/S0218196713400171

• Supercharacter table
• triangular groups
• finite fields
• symmetric functions

We give an LU-decomposition of the supercharacter table of the group of n x n unipotent upper triangular matrices over F-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 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.

• 出版日期2013-6