Enriched set-valued P-partitions and shifted stable Grothendieck polynomials
We introduce an enriched analogue of Lam and Pylyavskyy’s theory of set-valued P -partitions. An an application, we construct a K -theoretic version of Stembridge’s Hopf algebra of peak quasisymmetric functions. We show that the symmetric part of this algebra is generated by Ikeda and Naruse’s shift...
Saved in:
Published in | Mathematische Zeitschrift Vol. 299; no. 3-4; pp. 1929 - 1972 |
---|---|
Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.12.2021
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | We introduce an enriched analogue of Lam and Pylyavskyy’s theory of set-valued
P
-partitions. An an application, we construct a
K
-theoretic version of Stembridge’s Hopf algebra of peak quasisymmetric functions. We show that the symmetric part of this algebra is generated by Ikeda and Naruse’s shifted stable Grothendieck polynomials. We give the first proof that the natural skew analogues of these power series are also symmetric. A central tool in our constructions is a “
K
-theoretic” Hopf algebra of labeled posets, which may be of independent interest. Our results also lead to some new explicit formulas for the involution
ω
on the ring of symmetric functions. |
---|---|
ISSN: | 0025-5874 1432-1823 |
DOI: | 10.1007/s00209-021-02751-5 |