Integrality and Specialized Symmetric Functions
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912532478820352 |
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| author | Berele, Allan |
| author_facet | Berele, Allan |
| contents | Given $d_1,\ldots,d_k$ in the field $F$, there is a weighted trace function $F^k\rightarrow F$ given by $tr(x_1,\ldots,x_k)=\sum d_ix_i$. We prove that $F^k$ satisfies trace identities of the forms $α(d_1,\ldots,d_k) x^N=$ a linear combination of terms with lower powers of $x$; and $tr(y_1)\cdots tr(y_n)=$ a linear combination of terms with fewer traces. The approach uses specialized symmetric functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_08018 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integrality and Specialized Symmetric Functions Berele, Allan Rings and Algebras 16R30 (primary), 05E05 (Secondary) Given $d_1,\ldots,d_k$ in the field $F$, there is a weighted trace function $F^k\rightarrow F$ given by $tr(x_1,\ldots,x_k)=\sum d_ix_i$. We prove that $F^k$ satisfies trace identities of the forms $α(d_1,\ldots,d_k) x^N=$ a linear combination of terms with lower powers of $x$; and $tr(y_1)\cdots tr(y_n)=$ a linear combination of terms with fewer traces. The approach uses specialized symmetric functions. |
| title | Integrality and Specialized Symmetric Functions |
| topic | Rings and Algebras 16R30 (primary), 05E05 (Secondary) |
| url | https://arxiv.org/abs/2508.08018 |