Closed $k$-Schur Katalan functions as $K$-homology Schubert representatives of the affine Grassmannian

Takeshi Ikeda, Shinsuke Iwao, Satoshi Naito

Recently, Blasiak-Morse-Seelinger introduced symmetric functions called Katalan functions, and proved that the $K$-theoretic $k$-Schur functions due to Lam-Schilling-Shimozono form…