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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.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons