Schur Superpolynomials: Combinatorial Definition and Pieri Rule
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Schur Superpolynomials: Combinatorial Definition and Pieri Rule
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| Creator |
Blondeau-Fournier, O.
Mathieu, P. |
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| Description |
Schur superpolynomials have been introduced recently as limiting cases of the Macdonald superpolynomials. It turns out that there are two natural super-extensions of the Schur polynomials: in the limit q=t=0 and q=t→∞, corresponding respectively to the Schur superpolynomials and their dual. However, a direct definition is missing. Here, we present a conjectural combinatorial definition for both of them, each being formulated in terms of a distinct extension of semi-standard tableaux. These two formulations are linked by another conjectural result, the Pieri rule for the Schur superpolynomials. Indeed, and this is an interesting novelty of the super case, the successive insertions of rows governed by this Pieri rule do not generate the tableaux underlying the Schur superpolynomials combinatorial construction, but rather those pertaining to their dual versions. As an aside, we present various extensions of the Schur bilinear identity.
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| Date |
2019-02-12T18:11:31Z
2019-02-12T18:11:31Z 2015 |
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| Type |
Article
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| Identifier |
Schur Superpolynomials: Combinatorial Definition and Pieri Rule / O. Blondeau-Fournier, P. Mathieu // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 14 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 05E05 DOI:10.3842/SIGMA.2015.021 http://dspace.nbuv.gov.ua/handle/123456789/146998 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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