A representation-theoretic interpretation of the Schur expansion of two-row genomic Schur functions
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908995431694336 |
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| author | Kim, Young-Hun |
| author_facet | Kim, Young-Hun |
| contents | Genomic Schur functions were introduced by Pechenik and Yong in connection with the $K$-theory of Grassmannians. Pechenik proved that genomic Schur functions admit a positive expansion in the basis of fundamental quasisymmetric functions and, for partitions with two parts, a positive expansion in the Schur basis. Later, Kim and Yoo constructed $0$-Hecke modules associated with genomic Schur functions and conjectured that the latter expansion admits a representation-theoretic interpretation in terms of $0$-Hecke modules. In this paper, we prove the conjecture of Kim and Yoo, thereby obtaining a representation-theoretic interpretation of the Schur expansion in the two-row case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24454 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A representation-theoretic interpretation of the Schur expansion of two-row genomic Schur functions Kim, Young-Hun Combinatorics Representation Theory Genomic Schur functions were introduced by Pechenik and Yong in connection with the $K$-theory of Grassmannians. Pechenik proved that genomic Schur functions admit a positive expansion in the basis of fundamental quasisymmetric functions and, for partitions with two parts, a positive expansion in the Schur basis. Later, Kim and Yoo constructed $0$-Hecke modules associated with genomic Schur functions and conjectured that the latter expansion admits a representation-theoretic interpretation in terms of $0$-Hecke modules. In this paper, we prove the conjecture of Kim and Yoo, thereby obtaining a representation-theoretic interpretation of the Schur expansion in the two-row case. |
| title | A representation-theoretic interpretation of the Schur expansion of two-row genomic Schur functions |
| topic | Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2604.24454 |