Quantum K-theory of Lagrangian Grassmannian via parabolic Peterson isomorphism

We study Schubert calculus in the torus-equivariant quantum K-ring of the Lagrangian Grassmannian LG(n). Our main tool is the K-theoretic Peterson map due to Kato. The map is from the (localized) equivariant K-homology ring K*T(GrG) of the affine Grassmannian GrG of the symplectic group G=Sp₂ₙ(C) to the (localized) torus-equivariant quantum K-ring QKT(LG(n)). We determine explicitly the kernel of this map.