Pieri rule for classical groups, a new perspective

TL;DR

This paper offers a new perspective on Pieri rules for classical groups, extends Kostant's tensor product theorem, and establishes equivalences between these rules and branching rules for general linear groups.

Contribution

It introduces a novel approach to Pieri rules, extends a key theorem of Kostant, and links these concepts to branching rules in a unified framework.

Findings

Pieri rule form is equivalent to the converse of extended Kostant's theorem.

Pieri rule is equivalent to the branching rule for general linear groups.

Provides a new perspective connecting classical group rules and tensor product theorems.

Abstract

We study a new perspective on a certain Pieri rules for classical groups. Furthermore, we extend a fundamental theorem of Kostant concerning tensor products for classical groups. We show that a certain form of the Pieri rule is equivalent to the converse of this extended version of Kostant's theorem. In addition, we show an equivalence between the Pieri rule and the branching rule for general linear groups.