Expanding K-theoretic Schur Q-functions
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866909088462405632 |
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| author | Chiu, Yu-Cheng Marberg, Eric |
| author_facet | Chiu, Yu-Cheng Marberg, Eric |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_08993 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Expanding K-theoretic Schur Q-functions Chiu, Yu-Cheng Marberg, Eric Combinatorics 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. |
| title | Expanding K-theoretic Schur Q-functions |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2111.08993 |