Geodesic
Quantum Knizhnik--Zamolodchikov equation, totally symmetric
Teoretičeskaâ i matematičeskaâ fizika, Tome 154 (2008) no. 3, pp. 387-408

Voir la notice de l'article provenant de la source Math-Net.Ru

We present multiple-residue integral formulas for partial sums in the basis of link patterns of the polynomial solution of the level-$1$ $U_q(\widehat{\mathfrak{sl}_2})$ quantum Knizhnik–Zamolodchikov equation at arbitrary values of the quantum parameter $q$. These formulas allow rewriting and generalizing a recent conjecture of Di Francesco connecting these sums to generating polynomials for weighted totally symmetric self-complementary plane partitions. We reduce the corresponding conjectures to a single integral identity, yet to be proved.
Keywords: loop model, combinatorics, quantum integrability. 
@article{TMF_2008_154_3_a0,
     author = {P. Zinn-Justin and Ph. Di Francesco},
     title = {Quantum {Knizhnik--Zamolodchikov} equation, totally symmetric},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {387--408},
     publisher = {mathdoc},
     volume = {154},
     number = {3},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_154_3_a0/}
}
TY  - JOUR
AU  - P. Zinn-Justin
AU  - Ph. Di Francesco
TI  - Quantum Knizhnik--Zamolodchikov equation, totally symmetric
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2008
SP  - 387
EP  - 408
VL  - 154
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2008_154_3_a0/
LA  - ru
ID  - TMF_2008_154_3_a0
ER  - 
%0 Journal Article
%A P. Zinn-Justin
%A Ph. Di Francesco
%T Quantum Knizhnik--Zamolodchikov equation, totally symmetric
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2008
%P 387-408
%V 154
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2008_154_3_a0/
%G ru
%F TMF_2008_154_3_a0
P. Zinn-Justin; Ph. Di Francesco. Quantum Knizhnik--Zamolodchikov equation, totally symmetric. Teoretičeskaâ i matematičeskaâ fizika, Tome 154 (2008) no. 3, pp. 387-408. http://geodesic.mathdoc.fr/item/TMF_2008_154_3_a0/