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SUMMARY:Spin chains and totally symmetric alternating sign matrices
DTSTART:20260416T120000Z
DTEND:20260416T130000Z
DTSTAMP:20260501T102100Z
UID:indico-event-5806@agenda.irmp.ucl.ac.be
DESCRIPTION:Speakers: Christian Walmsley Hagendorf (UCLouvain/IRMP/GPP)\n\
 nAlternating sign matrices are central objects in enumerative combinatoric
 s and closely related to the six-vertex model of statistical mechanics. To
 tally symmetric alternating sign matrices (TSASMs) form a highly constrain
 ed symmetry class whose enumeration is only partially understood. In this 
 talk\, I describe a connection between TSASM enumeration and a distinguish
 ed eigenvector of an integrable lattice model called the open XXZ spin cha
 in. \nThis eigenvector arises from a Laurent-polynomial solution of the b
 oundary quantum Knizhnik-Zamolodchikov (bqKZ) equations. It leads to a mul
 tivariate Laurent-polynomial generalisation of the sum of the eigenvector'
 s entries\, which is uniquely characterised by a set of algebraic properti
 es.\nWe show that a suitable partition function of a six-vertex model asso
 ciated with TSASMs satisfies the same properties. By unique characterisati
 on\, this partition function coincides with the generalised sum of the eig
 envector's entries. As a consequence\, TSASM enumeration can be studied us
 ing the bqKZ solution. In particular\, this connection yields a constant t
 erm formula for the number of TSASMs of arbitrary order.\n\nhttps://agenda
 .irmp.ucl.ac.be/event/5806/
LOCATION:B/2nd floor-B.203 - Seminar room (Marc de Hemptinne (chemin du Cy
 clotron\, 2\, Louvain-la-Neuve))
URL:https://agenda.irmp.ucl.ac.be/event/5806/
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