A dual approach to structure constants for K-theory of Grassmannians
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020)
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The problem of computing products of Schubert classes in the cohomology ring can be formulated as theproblem of expanding skew Schur polynomial into the basis of ordinary Schur polynomials. We reformulate theproblem of computing the structure constants of the Grothendieck ring of a Grassmannian variety with respect to itsbasis of Schubert structure sheaves in a similar way; we address the problem of expanding the generating functions forskew reverse-plane partitions into the basis of polynomials which are Hall-dual to stable Grothendieck polynomials. From this point of view, we produce a chain of bijections leading to Buch’s K-theoretic Littlewood-Richardson rule.
@article{DMTCS_2020_special_379_a43,
author = {Li, Huilan and Morse, Jennifer and Shields, Pat},
title = {A dual approach to structure constants for {K-theory} of {Grassmannians}},
journal = {Discrete mathematics & theoretical computer science},
year = {2020},
volume = {DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)},
doi = {10.46298/dmtcs.6361},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6361/}
}
TY - JOUR AU - Li, Huilan AU - Morse, Jennifer AU - Shields, Pat TI - A dual approach to structure constants for K-theory of Grassmannians JO - Discrete mathematics & theoretical computer science PY - 2020 VL - DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) UR - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6361/ DO - 10.46298/dmtcs.6361 LA - en ID - DMTCS_2020_special_379_a43 ER -
%0 Journal Article %A Li, Huilan %A Morse, Jennifer %A Shields, Pat %T A dual approach to structure constants for K-theory of Grassmannians %J Discrete mathematics & theoretical computer science %D 2020 %V DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) %U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6361/ %R 10.46298/dmtcs.6361 %G en %F DMTCS_2020_special_379_a43
Li, Huilan; Morse, Jennifer; Shields, Pat. A dual approach to structure constants for K-theory of Grassmannians. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020). doi: 10.46298/dmtcs.6361
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