AG Lie-Gruppen: A. Kosyak, Univ. Kyiv, Ukraine: Knots, Braids and Quantum groups

Knots, Braids and Quantum groups Vortragender: Alexandre Kosyak, Institute of
Mathematics, Kyiv, Ukraine Abstract: We will give the list of terms used in
knot theory, define the braid groups B_n, and indicate the connection between
knots, braids and quantum groups on the example of q-Pascal triangle. These
results generalize the results by Tuba and Wenzl (2001) of low dimensional
representations of B_3. The two-parameter Lawrence (1990), or Lawrence-Krammer
(2002), representations of B_n were used to prove that the Braid groups B_n
are linear: Krammer for B_4 (2002), Bigelow for all B_n (2001). We show in
addition that the Lawrence representation of B_n is a quantization of the
symmetric square of the Burau representation.