Peterson isomorphism in K-theory and relativistic toda lattice

Takeshi Ikeda, Shinsuke Iwao, Toshiaki Maeno

研究成果: Article査読

抄録

The K-homology ring of the affine Grassmannian of SLn(C) was studied by Lam, Schilling, and Shimozono. It is realized as a certain concrete Hopf subring of the ring of symmetric functions. On the other hand, for the quantum K-theory of the flag variety Fln, Kirillov and Maeno provided a conjectural presentation based on the results obtained by Givental and Lee. We construct an explicit birational morphism between the spectrums of these two rings. Our method relies on Ruijsenaars's relativistic Toda lattice with unipotent initial condition. From this result, we obtain a K-theory analogue of the so-called Peterson isomorphism for (co)homology. We provide a conjecture on the detailed relationship between the Schubert bases, and, in particular, we determine the image of Lenart-Maeno's quantum Grothendieck polynomial associated with a Grassmannian permutation.

本文言語English
ページ(範囲)6421-6462
ページ数42
ジャーナルInternational Mathematics Research Notices
2020
19
DOI
出版ステータスPublished - 2021
外部発表はい

ASJC Scopus subject areas

  • Mathematics(all)

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