Indecomposable Objects of $\underset{‾}{Rep}(G{L}_t)$ in Terms of Exterior Powers of the Tautological Object and its Dual

The purpose of this short note is to understand the Grothendieck ring of the Deligne category $\underset{‾}{\text{Rep}}(G{L}_t)$. We give a formula for the class of an indecomposable object in terms of exterior powers of the tautological object and its dual.