An elementary construction of the ring of dual $K$-$Q$-cancellation property
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915452628762624 |
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| author | Iwao, Shinsuke |
| author_facet | Iwao, Shinsuke |
| contents | This paper presents an elementary introduction on $K$-theoretic $Q$-functions, which were introduced by Ikeda and Naruse in 2013. These functions, which serve as $K$-theoretic analogs of Schur $Q$-functions, are known to possess combinatorial and algebraic constructions. In a 2022 paper, the author introduced ``$β$-deformed power-sums" to provide a simpler, more algebraic construction of these functions. Since the original approach relies on fermionic operators and vacuum expectation values, this paper presents a more accessible, purely algebraic treatment, following the exposition of Schur $Q$-functions in Macdonald's standard textbook. We also show that the algebra of dual $Q$-cancellation property with integer coefficients is generated by dual $K$-$Q$-functions associated with an odd row partition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14484 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An elementary construction of the ring of dual $K$-$Q$-cancellation property Iwao, Shinsuke Combinatorics K-Theory and Homology 05E05, 19L47, 14M15 This paper presents an elementary introduction on $K$-theoretic $Q$-functions, which were introduced by Ikeda and Naruse in 2013. These functions, which serve as $K$-theoretic analogs of Schur $Q$-functions, are known to possess combinatorial and algebraic constructions. In a 2022 paper, the author introduced ``$β$-deformed power-sums" to provide a simpler, more algebraic construction of these functions. Since the original approach relies on fermionic operators and vacuum expectation values, this paper presents a more accessible, purely algebraic treatment, following the exposition of Schur $Q$-functions in Macdonald's standard textbook. We also show that the algebra of dual $Q$-cancellation property with integer coefficients is generated by dual $K$-$Q$-functions associated with an odd row partition. |
| title | An elementary construction of the ring of dual $K$-$Q$-cancellation property |
| topic | Combinatorics K-Theory and Homology 05E05, 19L47, 14M15 |
| url | https://arxiv.org/abs/2508.14484 |