Colored HOMFLY Polynomials as Multiple Sums over Paths or Standard Young Tableaux
المؤلفون المشاركون
Morozov, A.
Morozov, And.
Anokhina, A.
Mironov, Andrei D.
المصدر
Advances in High Energy Physics
العدد
المجلد 2013، العدد 2013 (31 ديسمبر/كانون الأول 2013)، ص ص. 1-12، 12ص.
الناشر
Hindawi Publishing Corporation
تاريخ النشر
2013-10-23
دولة النشر
مصر
عدد الصفحات
12
التخصصات الرئيسية
الملخص EN
If a knot is represented by an m-strand braid, then HOMFLY polynomial in representation R is a sum over characters in all representations Q∈R⊗m.
Coefficients in this sum are traces of products of quantum ℛ^-matrices along the braid, but these matrices act in the space of intertwiners, and their size is equal to the multiplicity MRQ of Q in R⊗m.
If R is the fundamental representation R=[1]=□, then M□Q is equal to the number of paths in representation graph, which lead from the fundamental vertex □ to the vertex Q.
In the basis of paths the entries of the m-1 relevant ℛ^-matrices are associated with the pairs of paths and are nonvanishing only when the two paths either coincide or differ by at most one vertex, as a corollary ℛ^-matrices consist of just 1×1 and 2×2 blocks, given by very simple explicit expressions.
If cabling method is used to color the knot with the representation R, then the braid has as many as m|R| strands; Q have a bigger size m|R|, but only paths passing through the vertex R are included into the sums over paths which define the products and traces of the m|R|-1 relevant ℛ^-matrices.
In the case of SU(N), this path sum formula can also be interpreted as a multiple sum over the standard Young tableaux.
By now it provides the most effective way for evaluation of the colored HOMFLY polynomials, conventional or extended, for arbitrary braids.
نمط استشهاد جمعية علماء النفس الأمريكية (APA)
Anokhina, A.& Mironov, Andrei D.& Morozov, A.& Morozov, And.. 2013. Colored HOMFLY Polynomials as Multiple Sums over Paths or Standard Young Tableaux. Advances in High Energy Physics،Vol. 2013, no. 2013, pp.1-12.
https://search.emarefa.net/detail/BIM-509203
نمط استشهاد الجمعية الأمريكية للغات الحديثة (MLA)
Anokhina, A.…[et al.]. Colored HOMFLY Polynomials as Multiple Sums over Paths or Standard Young Tableaux. Advances in High Energy Physics No. 2013 (2013), pp.1-12.
https://search.emarefa.net/detail/BIM-509203
نمط استشهاد الجمعية الطبية الأمريكية (AMA)
Anokhina, A.& Mironov, Andrei D.& Morozov, A.& Morozov, And.. Colored HOMFLY Polynomials as Multiple Sums over Paths or Standard Young Tableaux. Advances in High Energy Physics. 2013. Vol. 2013, no. 2013, pp.1-12.
https://search.emarefa.net/detail/BIM-509203
نوع البيانات
مقالات
لغة النص
الإنجليزية
الملاحظات
Includes bibliographical references
رقم السجل
BIM-509203
قاعدة معامل التأثير والاستشهادات المرجعية العربي "ارسيف Arcif"
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