Alladi Ramakrishnan Hall

On the column sums and total sum of a character table

Digjoy Paul

IISc

Column sums of the character table of a finite group are always integers (non-negative for Weyl groups). We conjecture for a finite group that the first column sum dominates the sum of the remaining columns. For Weyl groups, we prove the conjecture, give a criterion for when a column sum becomes zero, and obtain generating functions for numbers of such columns. The total sum of the character table of the symmetric group is another interesting statistic as it equals the sum of symmetric Kronecker coefficients. We compute the generating function of total sums for generalized symmetric groups. This is joint work with Arvind Ayyer and Hiranya Kishore Dey.