On algebraic equations satisfied by hypergeometric solutions of the qKZ equation

1997/10/31 by E. Mukhin, Mukhin, E., A. Varchenko +1
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #q-alg

paper · pdf · doi:10.48550/arxiv.q-alg/9710040

Latex, 20 pages

arxiv created 1997/11/02 · arxiv updated 2009/11/30

Abstract

We consider the sl(2) quantized Knizhnik-Zamolodchikov equation (qKZ), defined in terms of rational R-matrices. The properties of the equation change when the step of the equation takes a resonance value. In this case the discrete connection defined by the qKZ equation has a invariant subbundle which we call the subbundle of quantized conformal blocks. Solutions of the qKZ equation were constructed in [TV1], [MV1] in terms of multidimensional hypergeometric integrals. In this paper we show that for a resonance step all hypergeometric solutions take values in the subbundle of quantized conformal blocks, moreover the values span the subbundle of quantized conformal blocks under certain conditions. We describe the space of hypergeometric solutions in terms of the quantum group U_qsl(2).

Related

• Completeness of the Hypergeometric Solutions of the qKZ Equation at Level Zero
• Resonance relations, holomorphic trace functions and hypergeometric solutions to qKZB and Macdonald-Ruijsenaars equations
• The Quantized Knizhnik-Zamolodchikov Equation in Tensor Products of Irreducible sl(2)-Modules
• Functorial properties of the hypergeometric map
• Hypergeometric Solutions of the qKZ Equation at Level Zero