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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2506.18338 |
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| _version_ | 1866909659678375936 |
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| author | Arthamonov, S. Shakirov, Sh. Yan, W. |
| author_facet | Arthamonov, S. Shakirov, Sh. Yan, W. |
| contents | Genus 2 Macdonald polynomials $Ψ^{(q,t)}_{j_1,j_2,j_3}$ generalize ordinary Macdonald polynomials in several aspects. First, they provide common eigenfunctions for commuting difference operators that generalize the Macdonald difference operators of type $A_1$. Second, the algebra generated by these difference operators together with multiplication operators admits an action of genus 2 mapping class group (MCG) that generalizes the well-known action of $SL(2,{\mathbb Z})$ for ordinary Macdonald polynomials. In this paper, one more important aspect of Macdonald theory is considered: the Cauchy identities. We construct a genus 2 generalization of Cauchy identities in the particular case when $t=q=1$, i.e. for genus 2 Schur polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_18338 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cauchy identities for genus 2 Schur polynomials Arthamonov, S. Shakirov, Sh. Yan, W. Representation Theory Mathematical Physics 16G30, 33E30, 81R12 Genus 2 Macdonald polynomials $Ψ^{(q,t)}_{j_1,j_2,j_3}$ generalize ordinary Macdonald polynomials in several aspects. First, they provide common eigenfunctions for commuting difference operators that generalize the Macdonald difference operators of type $A_1$. Second, the algebra generated by these difference operators together with multiplication operators admits an action of genus 2 mapping class group (MCG) that generalizes the well-known action of $SL(2,{\mathbb Z})$ for ordinary Macdonald polynomials. In this paper, one more important aspect of Macdonald theory is considered: the Cauchy identities. We construct a genus 2 generalization of Cauchy identities in the particular case when $t=q=1$, i.e. for genus 2 Schur polynomials. |
| title | Cauchy identities for genus 2 Schur polynomials |
| topic | Representation Theory Mathematical Physics 16G30, 33E30, 81R12 |
| url | https://arxiv.org/abs/2506.18338 |