Permutation-Equivariant Quantum K-Theory of the Quintic Singularity

Abstract: We compute the genus-0 permutation-equivariant quantum K-theory of the singularity of the quintic polynomial, parallel to Givental--Lee's quantum K-theory of the quintic threefold. We obtain a generating function which recovers the entire 25-dimensional space of solutions to the $q$-difference equation satisfied by the permutation-equivariant K-theoretic $I$-function of the quintic.