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Knots in Washington XXV dedicated to Herbert Seifert on his 100 birthday. Conference on Knot Theory and its Ramifications
December 7-9, 2007
George Washington University
Washington, DC, USA

Organizers
Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Alexander Shumakovitch (GWU), Dan Silver (U. South Al.), Hao Wu (GWU)

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The Gram determinant of the type-B Temperley-Lieb algebra
by
Qi Chen
Winston-Salem State University
Coauthors: Jozef Przytycki

The n-th type-B Temperley-Lieb algebra is the Kauffman bracket skein module of the annulus with 2n marks on one boundary. It admitts a symmetric bilinear form. The Gram determinat Dn of this bilinear form is conjectured, by Dabkowski and Przytycki, to be equivalent to the determinant of the type-B matrix of chromatic joints invested by Rodica Simon. Barad gave a formula for Dn. In this talk we will provide a proof for this formula. The proof uses the connection between the Kaffman bracket skein module and the representaion theory of sl2.

Date received: November 29, 2007

Copyright © 2007 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cavo-11.