Primed decomposition tableaux and extended queer crystals
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915701976989696 |
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| author | Marberg, Eric Tong, Kam Hung |
| author_facet | Marberg, Eric Tong, Kam Hung |
| contents | Our previous work introduced a category of extended queer crystals, whose connected normal objects have unique highest weight elements and characters that are Schur $Q$-polynomials. The initial models for such crystals were based on semistandard shifted tableaux. Here, we introduce a simpler construction using certain "primed" decomposition tableaux, which slightly generalize the decomposition tableaux used in work of Grantcharov et al. This leads to a new, shorter proof of the highest weight properties of the normal subcategory of extended queer crystals. Along the way, we analyze a primed extension of Grantcharov et al.'s insertion scheme for decomposition tableaux. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_15409 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Primed decomposition tableaux and extended queer crystals Marberg, Eric Tong, Kam Hung Combinatorics Representation Theory Our previous work introduced a category of extended queer crystals, whose connected normal objects have unique highest weight elements and characters that are Schur $Q$-polynomials. The initial models for such crystals were based on semistandard shifted tableaux. Here, we introduce a simpler construction using certain "primed" decomposition tableaux, which slightly generalize the decomposition tableaux used in work of Grantcharov et al. This leads to a new, shorter proof of the highest weight properties of the normal subcategory of extended queer crystals. Along the way, we analyze a primed extension of Grantcharov et al.'s insertion scheme for decomposition tableaux. |
| title | Primed decomposition tableaux and extended queer crystals |
| topic | Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2312.15409 |