Explicit decomposition of certain induced representations of the general linear group

TL;DR

This paper presents experimental results on decomposing certain induced representations of the general linear group over local non-archimedean fields, focusing on parabolic induction of tensor products of irreducible representations.

Contribution

It provides new experimental insights into the decomposition of parabolic inductions in the Grothendieck group for GL_n representations.

Findings

Experimental results on decomposition patterns

Insights into parabolic induction of tensor products

Contributions to understanding representation structure

Abstract

We provide some experimental results on the decomposition of the parabolic induction of $\pi\otimes\pi$ in the Grothendieck group where $\pi$ is an irreducible representation of $GL_n$ over a local non-archimedean field.