Degeneracy loci classes in K-theory — determinantal and Pfaffian formula

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 Pra...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2017-11, Vol.320, p.115-156
Main Authors: Hudson, Thomas, Ikeda, Takeshi, Matsumura, Tomoo, Naruse, Hiroshi
Format: Article
Language:English
Subjects:
Determinant
K-theory
Pfaffian
Schubert calculus
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Summary: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.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2017.08.038