P Di Francesco and P Zinn-Justin 2005 J. Phys. A: Math. Gen. 38 L815 doi:10.1088/0305-4470/38/48/L02
The quantum Knizhnik–Zamolodchikov equation, generalized Razumov–Stroganov sum rules and extended Joseph polynomials
FREE ARTICLEP Di Francesco1 and P Zinn-Justin2
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We prove higher rank analogues of the Razumov–Stroganov sum rule for the ground state of the O(1) loop model on a semi-infinite cylinder: we show that a weighted sum of components of the ground state of the Ak−1 IRF model yields integers that generalize the numbers of alternating sign matrices. This is done by constructing minimal polynomial solutions of the level 1 
quantum Knizhnik–Zamolodchikov equations, which may also be interpreted as quantum incompressible q-deformations of quantum Hall effect wavefunctions at filling fraction ν = k. In addition to the generalized Razumov–Stroganov point q = −eiπ/k+1, another combinatorially interesting point is reached in the rational limit q → −1, where we identify the solution with extended Joseph polynomials associated with the geometry of upper triangular matrices with vanishing kth power.
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Issue 48 (2 December 2005)
Received 23 September 2005
Published 16 November 2005
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The quantum Knizhnik–Zamolodchikov equation, generalized Razumov–Stroganov sum rules and extended Joseph polynomials
P Di Francesco and P Zinn-Justin 2005 J. Phys. A: Math. Gen. 38 L815
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