Minuscule Relations in Quantum $K$-Theory of Flag Varieties

We study the quantum $K$-theory of the flag variety $G\mathrm{/}B$. For each minuscule fundamental weight $\varpi$, we construct an explicit relation in the torus-equivariant quantum $K$-theory $Q{K}_T(G\mathrm{/}B)$. The relation can be regarded as a quantum deformation of the character of the irreducible representation with highest weight $\varpi$.