Polynomial KP and BKP $\tau$-functions and correlators
| Autor: | Harnad, J., Orlov, A. Yu. |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Annales Henri Poincar\'e 22, 3025-3049 (2021) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00023-021-01046-z |
| Popis: | Lattices of polynomial KP and BKP $\tau$-functions labelled by partitions, with the flow variables equated to finite power sums, as well as associated multipair KP and multipoint BKP correlation functions are expressed via generalizations of Jacobi's bialternant formula for Schur functions and Nimmo's Pfaffian ratio formula for Schur $Q$-functions. These are obtained by applying Wick's theorem to fermionic vacuum expectation value representations in which the infinite group element acting on the lattice of basis states stabilizes the vacuum. Comment: 26 pages. References updated. Notations for $Q_{\alpha}$ rendered more consistent. Statement and proof of Propositions 4.1 and 4.2 revised. Eq. (4.6) corrected. Typos corrected |
| Databáze: | arXiv |
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