2014/03/14 by Kazufumi Kimoto, Kimoto, Kazufumi · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #FOS: Mathematics #Random Matrices and Applications #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1403.3723
openalex publication_date 2014/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that certain weighted average of the alpha-determinant of a kn by kn matrix of the form A⊗11,k, the Kronecker product of a kn by n matrix A and 1 by k all one matrix 11,k, over permutations of kn letters is reduced to the k-wreath determinant of A up to constant. The constant is exactly given by the modified content polynomial for the Young diagram (kn). As a corollary, we give a `determinantal' formula for certain functions on the symmetric groups which are invariant under the left and right translation by a Young subgroup, especially the values of the Kostka numbers for rectangular shapes with arbitrary weight. This corollary gives a generalization of the formula of irreducible characters of the symmetric group for rectangular shapes due to Stanley.