Pfaffian Formulation of Schur's $Q$-functions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912240896049152 |
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| author | Graf, John Jing, Naihuan |
| author_facet | Graf, John Jing, Naihuan |
| contents | We introduce a Pfaffian formula that extends Schur's $Q$-functions $Q_λ$ to be indexed by compositions $λ$ with negative parts. This formula makes the Pfaffian construction more consistent with other constructions, such as the Young tableau and Vertex Operator constructions. With this construction, we develop a proof technique involving decomposing $Q_λ$ into sums indexed by partitions with removed parts. Consequently, we are able to prove several identities of Schur's $Q$-functions using only simple algebraic methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_13137 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pfaffian Formulation of Schur's $Q$-functions Graf, John Jing, Naihuan Combinatorics 05E05 We introduce a Pfaffian formula that extends Schur's $Q$-functions $Q_λ$ to be indexed by compositions $λ$ with negative parts. This formula makes the Pfaffian construction more consistent with other constructions, such as the Young tableau and Vertex Operator constructions. With this construction, we develop a proof technique involving decomposing $Q_λ$ into sums indexed by partitions with removed parts. Consequently, we are able to prove several identities of Schur's $Q$-functions using only simple algebraic methods. |
| title | Pfaffian Formulation of Schur's $Q$-functions |
| topic | Combinatorics 05E05 |
| url | https://arxiv.org/abs/2405.13137 |