Dimension formula for the space of relative symmetric polynomials of D_n with respect to any irreducible representation

TL;DR

This paper derives a formula and generating function to compute the dimension of the space of relative symmetric polynomials of the dihedral group D_n for all its irreducible representations, expanding understanding of symmetric polynomial structures.

Contribution

It introduces a comprehensive formula and generating function for the dimensions of relative symmetric polynomial spaces associated with all irreducible representations of D_n.

Findings

Provides explicit dimension formulas for all irreducible representations of D_n.

Develops a generating function to facilitate dimension calculations.

Enhances the theoretical framework for symmetric polynomials related to dihedral groups.

Abstract

We provide a formula and a generating function for the dimension of the vector space of relative symmetric polynomials of D_n for all its irreducible one-dimensional and two-dimensional representations which were defined originally by M. Shahryari.