@article{37065554d8e34bd685b4442f5ebf5807,
title = "Degeneracy loci classes in K-theory — determinantal and Pfaffian formula",
abstract = "We prove a determinantal formula that describes the K-theoretic degeneracy loci classes for Grassmann bundles. We further prove Pfaffian formulas for symplectic and odd orthogonal Grassmann bundles. The former generalizes Damon–Kempf–Laksov's determinantal formula, and the latter generalize Pragacz–Kazarian's formulas for the Chow ring.",
keywords = "Determinant, K-theory, Pfaffian, Schubert calculus",
author = "Thomas Hudson and Takeshi Ikeda and Tomoo Matsumura and Hiroshi Naruse",
note = "Funding Information: We would like to thank Leonardo Mihalcea and Anders Buch for their helpful comments on earlier versions of this manuscript. We are also grateful to the anonymous referee, whose careful observations and suggestions simplified the exposition and greatly improved the readability. A considerable part of this work developed while the first and third authors were affiliated to KAIST, which they would like to thank for the excellent working conditions. Part of this work developed while the first author was affiliated to POSTECH, which he would like to thank for the excellent working conditions. He would also like to gratefully acknowledge the support of the National Research Foundation of Korea (NRF) through the grants funded by the Korea government ( MSIP ) (ASARC, NRF-2007-0056093 ) and ( MSIP ) (No. 2011-0030044 ). The second author was supported by Grant-in-Aid for Scientific Research (C) 24540032 , 15K04832 . The third author was supported by Grant-in-Aid for Young Scientists (B) 16K17584 . The fourth author was supported by Grant-in-Aid for Scientific Research (C) 25400041 , (B) 16H03921 . Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",
year = "2017",
month = nov,
day = "7",
doi = "10.1016/j.aim.2017.08.038",
language = "English",
volume = "320",
pages = "115--156",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press Inc.",
}