Highest weight vectors of tensors
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915758245675008 |
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| author | Amanov, Alimzhan Yeliussizov, Damir |
| author_facet | Amanov, Alimzhan Yeliussizov, Damir |
| contents | We study highest weight vectors for symmetric and alternating spaces of tensors, whose dimensions are given by generalized Kronecker coefficients. We describe the algebraic relations for classical constructions of corresponding spanning sets of highest weight vectors. The proof is based on important duality that we discover for these highest weight spaces and vectors. As applications of duality, we also give conceptual interpretations to power expansions of Cayley's first hyperdeterminant and its dual exterior form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15413 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Highest weight vectors of tensors Amanov, Alimzhan Yeliussizov, Damir Combinatorics Representation Theory We study highest weight vectors for symmetric and alternating spaces of tensors, whose dimensions are given by generalized Kronecker coefficients. We describe the algebraic relations for classical constructions of corresponding spanning sets of highest weight vectors. The proof is based on important duality that we discover for these highest weight spaces and vectors. As applications of duality, we also give conceptual interpretations to power expansions of Cayley's first hyperdeterminant and its dual exterior form. |
| title | Highest weight vectors of tensors |
| topic | Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2504.15413 |