THE QUANTUM sl(n, ℂ) REPRESENTATION THEORY AND ITS APPLICATIONS

Title & Authors
THE QUANTUM sl(n, ℂ) REPRESENTATION THEORY AND ITS APPLICATIONS
Jeong, Myeong-Ju; Kim, Dong-Seok;

Abstract
In this paper, we study the quantum sl($\small{n}$) representation category using the web space. Specially, we extend sl($\small{n}$) web space for $\small{n{\geq}4}$ as generalized Temperley-Lieb algebras. As an application of our study, we find that the HOMFLY polynomial $\small{P_n(q)}$ specialized to a one variable polynomial can be computed by a linear expansion with respect to a presentation of the quantum representation category of sl($\small{n}$). Moreover, we correct the false conjecture [30] given by Chbili, which addresses the relation between some link polynomials of a periodic link and its factor link such as Alexander polynomial (\$n
Keywords
quantum sl($\small{n}$) representation theory;colored HOMFLY polynomial specialized to a one variable polynomial;periodic links;web spaces;
Language
English
Cited by
1.
On skein relations in class S theories, Journal of High Energy Physics, 2015, 2015, 6
2.
Webs and quantum skew Howe duality, Mathematische Annalen, 2014, 360, 1-2, 351
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