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We prove higher rank analogues of the Razumov--Stroganov sum rule for thegroundstate of the O(1) loop model on a semi-infinite cylinder: we show that aweighted sum of components of the groundstate of the A_{k-1} IRF model yieldsintegers that generalize the numbers of alternating sign matrices. This is doneby constructing minimal polynomial solutions of the level 1 U_q(\hat{sl(k)})quantum Knizhnik--Zamolodchikov equations, which may also be interpreted asquantum incompressible q-deformations of fractional quantum Hall effect wavefunctions at filling fraction nu=1/k. In addition to the generalizedRazumov--Stroganov point q=-e^{i pi/k+1}, another combinatorially interestingpoint is reached in the rational limit q -> -1, where we identify the solutionwith extended Joseph polynomials associated to the geometry of upper triangularmatrices with vanishing k-th power.Comment: v3: misprint fixed in eq (2.1

The quantum Knizhnik–Zamolodchikov equation, generalized Razumov–Stroganov sum rules and extended Joseph polynomials