Skew hook formula for d-complete posets via equivariant K-theory
Algebraic Combinatorics, Volume 2 (2019) no. 4, p. 541-571

Peterson and Proctor obtained a formula which expresses the multivariate generating function for P-partitions on a d-complete poset P as a product in terms of hooks in P. In this paper, we give a skew generalization of Peterson–Proctor’s hook formula, i.e. a formula for the generating function of (PF)-partitions for a d-complete poset P and an order filter F of P, by using the notion of excited diagrams. Our proof uses the Billey-type formula and the Chevalley-type formula in the equivariant K-theory of Kac–Moody partial flag varieties. This generalization provides an alternate proof of Peterson–Proctor’s hook formula. As the equivariant cohomology version, we derive a skew generalization of a combinatorial reformulation of Nakada’s colored hook formula for roots.

Received : 2018-03-11
Revised : 2018-12-06
Accepted : 2018-12-15
Published online : 2019-08-01
DOI : https://doi.org/10.5802/alco.54
Classification:  05A15,  06A07,  14N15,  19L47
Keywords: d-complete posets, hook formulas, P-partitions, Schubert calculus, equivariant K-theory
@article{ALCO_2019__2_4_541_0,
     author = {Naruse, Hiroshi and Okada, Soichi},
     title = {Skew hook formula for $d$-complete posets via equivariant $K$-theory},
     journal = {Algebraic Combinatorics},
     publisher = {MathOA foundation},
     volume = {2},
     number = {4},
     year = {2019},
     pages = {541-571},
     doi = {10.5802/alco.54},
     language = {en},
     url = {https://alco.centre-mersenne.org/item/ALCO_2019__2_4_541_0}
}
Skew hook formula for $d$-complete posets via equivariant $K$-theory. Algebraic Combinatorics, Volume 2 (2019) no. 4, pp. 541-571. doi : 10.5802/alco.54. https://alco.centre-mersenne.org/item/ALCO_2019__2_4_541_0/

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