The purpose of this short note is to understand the Grothendieck ring of the Deligne category $\underline{\text{Rep}}(GL_t)$. We give a formula for the class of an indecomposable object in terms of exterior powers of the tautological object and its dual.
On exterior powers of reflection representations
Schur-Weyl duality for Deligne categories
Categorical actions and multiplicities in the Deligne category $\underline{Rep}(GL_t)$
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