Racah coefficients and extended HOMFLY polynomials for all 5-, 6- and 7-strand braidsстатья
Статья опубликована в высокорейтинговом журнале
Информация о цитировании статьи получена из
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Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 14 сентября 2013 г.
Авторы:
Anokhina A.,
Mironov A.,
Morozov A.,
Morozov An
Аннотация:Basing on evaluation of the Racah coefficients for SU_q(3) (which supported the earlier conjecture of their universal form) we derive explicit formulas for all the 5-, 6- and 7-strand Wilson averages in the fundamental representation of arbitrary SU(N) group (the HOMFLY polynomials). As an application, we list the answers for all 5-strand knots with 9 crossings. In fact, the 7-strand formulas are sufficient to reproduce all the HOMFLY polynomials from the katlas.org: they are all described at once by a simple explicit formula with a very transparent structure. Moreover, would the formulas for the relevant SU_q(3) Racah coefficients remain true for all other quantum groups, the paper provides a complete description of the fundamental HOMFLY polynomials for all braids with any number of strands.