ALGEBRAIC COMBINATORICS

no. 6
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, Volume 6 (2023) no. 6, pp. 1419-1445.

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.

Received:
Revised:
Accepted:
Published online:
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
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Chiu, Yu-Cheng; Marberg, Eric. Expanding $K$-theoretic Schur $Q$-functions. Algebraic Combinatorics, Volume 6 (2023) no. 6, pp. 1419-1445. doi : 10.5802/alco.312. https://alco.centre-mersenne.org/articles/10.5802/alco.312/

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