Geodesic
Skew hook formula for d-complete posets via equivariant K-theory
Naruse, Hiroshi1 ; Okada, Soichi2
1Graduate School of Education, University of Yamanashi 4-4-37, Takeda, Kofu, Yamanashi 400-8510, Japan
2Graduate School of Mathematics, Nagoya University Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan
Algebraic Combinatorics, Tome 2 (2019) no. 4, pp. 541-571
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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 (P∖F)-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.

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DOI : 10.5802/alco.54
Classification : 05A15, 06A07, 14N15, 19L47
Keywords: $d$-complete posets, hook formulas, $P$-partitions, Schubert calculus, equivariant $K$-theory

Naruse, Hiroshi  1   ; Okada, Soichi  2

1 Graduate School of Education, University of Yamanashi 4-4-37, Takeda, Kofu, Yamanashi 400-8510, Japan
2 Graduate School of Mathematics, Nagoya University Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {Skew hook formula for $d$-complete posets via equivariant $K$-theory},
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     pages = {541--571},
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Naruse, Hiroshi; Okada, Soichi. Skew hook formula for $d$-complete posets via equivariant $K$-theory. Algebraic Combinatorics, Tome 2 (2019) no. 4, pp. 541-571. doi: 10.5802/alco.54

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