Tensor powers for non-simply laced Lie Algebras $B_2$ case

TL;DR

This paper investigates the decomposition of tensor powers of fundamental modules for the $B_2$ Lie algebra, using singular weight techniques and injection fan algorithms to analyze multiplicity coefficients.

Contribution

It introduces explicit multiplicity functions for $B_2$ tensor powers, revealing their dependence on highest weights and tensor power parameters, advancing understanding of these decompositions.

Findings

Explicit multiplicity functions for $B_2$ tensor powers

Dependence of multiplicities on highest weights and tensor powers

Properties of multiplicity coefficients for fundamental $B_2$ modules

Abstract

We study the decomposition problem for tensor powers of $B_2$-fundamental modules. To solve this problem singular weight technique and injection fan algorithms are applied. Properties of multiplicity coefficients are formulated in terms of multiplicity functions. These functions are constructed showing explicitly the dependence of multiplicity coefficients on the highest weight coordinates and the tensor power parameter. It is thus possible to study general properties of multiplicity coefficients for powers of the fundamental $B_2$- modules.