On the nonvanishing condition for $A_{\mathfrak q}(λ)$ of $U(p,q)$ in the mediocre range
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916580550508544 |
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| author | Du, Chengyu |
| author_facet | Du, Chengyu |
| contents | The modules $A_\mathfrak{q}(λ)$ of $U(p,q)$ can be parameterized by their annihilators and asymptotic supports, both of which can be identified using Young tableaux. Trapa developed an algorithm for determining the tableaux of the modules $A_\mathfrak{q}(λ)$ in the mediocre range, along with an equivalent condition to determine non-vanishing. The condition involves a combinatorial concept called the overlap, which is not straightforward to compute. In this paper, we establish a formula for the overlap and simplify the condition for ease of use. We then apply it to $K$-types and the Dirac index of $A_\mathfrak{q}(λ)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03216 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the nonvanishing condition for $A_{\mathfrak q}(λ)$ of $U(p,q)$ in the mediocre range Du, Chengyu Representation Theory The modules $A_\mathfrak{q}(λ)$ of $U(p,q)$ can be parameterized by their annihilators and asymptotic supports, both of which can be identified using Young tableaux. Trapa developed an algorithm for determining the tableaux of the modules $A_\mathfrak{q}(λ)$ in the mediocre range, along with an equivalent condition to determine non-vanishing. The condition involves a combinatorial concept called the overlap, which is not straightforward to compute. In this paper, we establish a formula for the overlap and simplify the condition for ease of use. We then apply it to $K$-types and the Dirac index of $A_\mathfrak{q}(λ)$. |
| title | On the nonvanishing condition for $A_{\mathfrak q}(λ)$ of $U(p,q)$ in the mediocre range |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2405.03216 |