# Algebraic structure of the q-Knizhnik-Zamolodchikov equation on a segment, partial sums and punctured plane partitions

Presented by:
J de Gier [Melbourne]
Date:
Tuesday 22nd April 2008 - 11:30 to 12:30
Venue:
INI Seminar Room 1
Abstract:

We show that solutions of the qKZ equation for the link pattern representation of the Temperley-Lieb algebra have the same structure as the canonical basis defined by Lusztig in tensor products of representation modules of U_q(sl_2). This structure gives in a natural way rise to consider partial sums over qKZ solutions. In the context of the Razumov-Stroganov conjecture we show that such partial sums over qKZ solutions of level one are related to weighted transpose complement cyclically symmetric plane partitions with a hole.