Counting SO(9)xSU(2) representations in coordinate independent state space of SU(2) Matrix Theory

TL;DR

This paper analyzes the representation structure of coordinate independent states in SU(2) Matrix theory by computing characters and decomposing them into SO(9) and SU(2) components.

Contribution

It introduces a method to decompose coordinate independent states into SO(9) x SU(2) representations using character calculations in SU(2) Matrix theory.

Findings

Identifies the specific SO(9) x SU(2) representations present in the state space.

Provides a systematic approach to decompose states into group representations.

Enhances understanding of the symmetry structure in SU(2) Matrix theory.

Abstract

We consider decomposition of coordinate independent states into SO(9)xSU(2) representations in SU(2) Matrix theory. To see what and how many representations appear in the decomposition, we compute the character, which is given by a trace over the coordinate independent states, and decompose it into the sum of products of SO(9) and SU(2) characters.