On the sign representations for the complex reflection groups $G(r,p,n)$

TL;DR

This paper provides a formula for the sign representations of complex reflection groups G(r,p,n) using a generalized Robinson-Schensted map, enhancing understanding of their representation theory.

Contribution

It introduces a new formula connecting sign representations of G(r,p,n) with a generalized Robinson-Schensted map, offering a novel computational approach.

Findings

Derived explicit formulas for sign representation values.

Connected representation theory with combinatorial algorithms.

Enhanced tools for analyzing complex reflection groups.

Abstract

We present a formula for the values of the sign representations of the complex reflection groups $G(r,p,n)$ in terms of its image under a generalized Robinson-Schensted map.