A local characterization of crystals for the quantum queer superalgebra
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866916675279912960 |
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| author | Assaf, Sami Oguz, Ezgi Kantarci |
| author_facet | Assaf, Sami Oguz, Ezgi Kantarci |
| contents | We define operators on semistandard shifted tableaux and use Stembridge's local characterization for regular graphs to prove they define a crystal structure. This gives a new proof that Schur $P$-polynomials are Schur positive. We define queer crystal operators (also called odd Kashiwara operators) to construct a connected queer crystal on semistandard shifted tableaux of a given shape. Using the tensor rule for queer crystals, this provides a new proof that products of Schur $P$-polynomials are Schur $P$-positive. Finally, to facilitate applications of queer crystals in the context of Schur $P$-positivity, we give local axioms for queer regular graphs, generalizing Stembridge's axioms, that partially characterize queer crystals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1803_06317 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | A local characterization of crystals for the quantum queer superalgebra Assaf, Sami Oguz, Ezgi Kantarci Combinatorics Representation Theory Primary 05E05, Secondary 05E10, 20G42 We define operators on semistandard shifted tableaux and use Stembridge's local characterization for regular graphs to prove they define a crystal structure. This gives a new proof that Schur $P$-polynomials are Schur positive. We define queer crystal operators (also called odd Kashiwara operators) to construct a connected queer crystal on semistandard shifted tableaux of a given shape. Using the tensor rule for queer crystals, this provides a new proof that products of Schur $P$-polynomials are Schur $P$-positive. Finally, to facilitate applications of queer crystals in the context of Schur $P$-positivity, we give local axioms for queer regular graphs, generalizing Stembridge's axioms, that partially characterize queer crystals. |
| title | A local characterization of crystals for the quantum queer superalgebra |
| topic | Combinatorics Representation Theory Primary 05E05, Secondary 05E10, 20G42 |
| url | https://arxiv.org/abs/1803.06317 |