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

Author:

Ikeda Takeshi,Iwao Shinsuke,Naito Satoshi

Abstract

Recently, Blasiak–Morse–Seelinger introduced symmetric func- tions called Katalan functions, and proved that the K K -theoretic k k -Schur functions due to Lam–Schilling–Shimozono form a subfamily of the Katalan functions. They conjectured that another subfamily of Katalan functions called closed k k -Schur Katalan functions is identified with the Schubert structure sheaves in the K K -homology of the affine Grassmannian. Our main result is a proof of this conjecture.

We also study a K K -theoretic Peterson isomorphism that Ikeda, Iwao, and Maeno constructed, in a nongeometric manner, based on the unipotent solution of the relativistic Toda lattice of Ruijsenaars. We prove that the map sends a Schubert class of the quantum K K -theory ring of the flag variety to a closed K K - k k -Schur Katalan function up to an explicit factor related to a translation element with respect to an antidominant coroot. In fact, we prove this map coincides with a map whose existence was conjectured by Lam, Li, Mihalcea, Shimozono, and proved by Kato, and more recently by Chow and Leung.

Funder

Japan Society for the Promotion of Science

Publisher

American Mathematical Society (AMS)

Reference40 articles.

1. Addison-Wesley Series in Mathematics;Atiyah, M. F.,2016

2. On the finiteness of quantum K-theory of a homogeneous space;Anderson, David;Int. Math. Res. Not. IMRN,2022

3. Equivariant homology and 𝐾-theory of affine Grassmannians and Toda lattices;Bezrukavnikov, Roman;Compos. Math.,2005

4. Graduate Texts in Mathematics;Björner, Anders,2005

5. 𝐾-theoretic Catalan functions;Blasiak, Jonah;Adv. Math.,2022

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