Explicit Calculations of Tensor Product Coefficients for E_7

TL;DR

This paper introduces a novel method for calculating tensor product coefficients of E_7 by decomposing characters into A_7 components, enabling feasible computation despite the large Weyl group sums.

Contribution

The paper presents a new approach to compute E_7 tensor product coefficients using character decomposition, reducing computational complexity.

Findings

Successfully decomposed E_7 characters into A_7 characters.

Enabled practical calculation of E_7 tensor product coefficients.

Provided a method to handle large Weyl group sums efficiently.

Abstract

We propose a new method to calculate coupling coefficients of E_7 tensor products. Our method is based on explicit use of E_7 characters in the definition of a tensor product. When applying Weyl character formula for E_7 Lie algebra, one needs to make sums over 2903040 elements of E_7 Weyl group. To implement such enormous sums, we show we have a way which makes their calculations possible. This will be accomplished by decomposing an E_7 character into 72 participating A_7 characters.