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Integrability of Hurwitz Partition Functions. I. Summaryстатья
Информация о цитировании статьи получена из
Web of Science,
Scopus
Дата последнего поиска статьи во внешних источниках: 14 сентября 2013 г.
- Авторы: Alexandrov A., Mironov A., Morozov A., Natanzon S.
- Журнал: Journal of Physics A
- Том: 45
- Номер: 4
- Год издания: 2012
- Первая страница: 1
- Последняя страница: 10
- DOI: 10.1088/1751-8113/45/4/045209
- Аннотация: Partition functions often become tau-functions of integrable hierarchies, if they are considered dependent on infinite sets of parameters called time variables. The Hurwitz partition functions Z = Sigma(R) d(R)(2-k) chi(R)R(t((1))) .... chi(R)(t((k)))exp(Sigma(n) xi(n)C(R)(n))depend on two types of such time variables, t and xi. KP/Toda integrability in t requires that k <= 2 and also that C(R)(n) are selected in a rather special way, in particular the naive cut-and-join operators are not allowed for n > 2. Integrability in. further restricts the choice of CR(n), forbidding, for example, the free cumulants. It also requires that k <= 1. The quasi-classical integrability (the WDVV equations) is naturally present in xi variables, but also requires a careful definition of the generating function.
- Добавил в систему: Натанзон Сергей Миронович