The sign character of the triagonal fermionic coinvariant ring

2025/01/17 by Lentfer, John · 1 citation
#05E05 #05E10 (Primary) 05A15 #05E16 #20C30 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2501.09920

Abstract

We determine the trigraded multiplicity of the sign character of the triagonal fermionic coinvariant ring R_n^(0,3). As a corollary, this proves a conjecture of Bergeron (2020) that the dimension of the sign character of R_n^(0,3) is n²-n+1. We also give an explicit formula for double hook characters in the diagonal fermionic coinvariant ring R_n^(0,2), and discuss methods towards calculating the sign character of R_n^(0,4). Finally, we give a multigraded refinement of a conjecture of Bergeron (2020) that the dimension of the sign character of the (1,3)-bosonic-fermionic coinvariant ring R_n^(1,3) is (1)/(2)F_3n, where F_n is a Fibonacci number.

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