Nahm's conjecture and Y-system

Details Nahm's conjecture and Y-system Nahm's conjecture and Y-system

2011-09-16

arxiv.org/abs/1109.3667v3

Mathematics

Quantum Algebra

ver.3, minor update (typos corrected)

Scientific paper

Nahm's conjecture relates $q$-hypergeometric modular functions to torsion elements in the Bloch group. An interesting class of such functions can be (conjecturally) obtained from a pair of Dynkin diagrams of $ADET$ type. Using properties of Y-system, we prove that for a matrix of the form $A=C(X) \otimes C(X')^{-1}$ where $C(X)$ and $C(X')$ are one of $ADET$ Cartan matrices, every solution of the equation $x=(1-x)^A$ gives rise to a torsion element of the Bloch group.

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