Geodesic
Expanding K-theoretic Schur Q-functions
Chiu, Yu-Cheng1 ; Marberg, Eric2
1 Department of Mathematics ETH Zürich Zürich, Switzerland
2 Department of Mathematics HKUST Clear Water Bay, Hong Kong
Algebraic Combinatorics, Tome 6 (2023) no. 6, pp. 1419-1445

Voir la notice de l'article provenant de la source Numdam

We derive several identities involving Ikeda and Naruse’s K-theoretic Schur P- and Q-functions. Our main result is a formula conjectured by Lewis and the second author which expands each K-theoretic Schur Q-function in terms of K-theoretic Schur P-functions. This formula extends to some more general identities relating the skew and dual versions of both power series. We also prove a shifted version of Yeliussizov’s skew Cauchy identity for symmetric Grothendieck polynomials. Finally, we discuss some conjectural formulas for the dual K-theoretic Schur P- and Q-functions of Nakagawa and Naruse. We show that one such formula would imply a basis property expected of the K-theoretic Schur Q-functions.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/alco.312
Classification : 05E05
Keywords: $K$-theoretic Schur $P$- and $Q$-functions, Cauchy identities, shifted tableaux, set-valued tableaux, plane partitions

Chiu, Yu-Cheng 1 ; Marberg, Eric 2

1 Department of Mathematics ETH Zürich Zürich, Switzerland
2 Department of Mathematics HKUST Clear Water Bay, Hong Kong
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
@article{ALCO_2023__6_6_1419_0,
     author = {Chiu, Yu-Cheng and Marberg, Eric},
     title = {Expanding $K$-theoretic {Schur} $Q$-functions},
     journal = {Algebraic Combinatorics},
     pages = {1419--1445},
     publisher = {The Combinatorics Consortium},
     volume = {6},
     number = {6},
     year = {2023},
     doi = {10.5802/alco.312},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5802/alco.312/}
}
TY  - JOUR
AU  - Chiu, Yu-Cheng
AU  - Marberg, Eric
TI  - Expanding $K$-theoretic Schur $Q$-functions
JO  - Algebraic Combinatorics
PY  - 2023
SP  - 1419
EP  - 1445
VL  - 6
IS  - 6
PB  - The Combinatorics Consortium
UR  - http://geodesic.mathdoc.fr/articles/10.5802/alco.312/
DO  - 10.5802/alco.312
LA  - en
ID  - ALCO_2023__6_6_1419_0
ER  - 
%0 Journal Article
%A Chiu, Yu-Cheng
%A Marberg, Eric
%T Expanding $K$-theoretic Schur $Q$-functions
%J Algebraic Combinatorics
%D 2023
%P 1419-1445
%V 6
%N 6
%I The Combinatorics Consortium
%U http://geodesic.mathdoc.fr/articles/10.5802/alco.312/
%R 10.5802/alco.312
%G en
%F ALCO_2023__6_6_1419_0
Chiu, Yu-Cheng; Marberg, Eric. Expanding $K$-theoretic Schur $Q$-functions. Algebraic Combinatorics, Tome 6 (2023) no. 6, pp. 1419-1445. doi: 10.5802/alco.312

Cité par Sources :