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Letters in Mathematical Physics

, Volume 105, Issue 1, pp 45–61 | Cite as

Tetrahedron Equation, Weyl Group, and Quantum Dilogarithm

  • Andrei Bytsko
  • Alexander Volkov
Article
  • 136 Downloads

Abstract

We derive a family of solutions to the tetrahedron equation using the RTT presentation of a two parametric quantized algebra of regular functions on an upper triangular subgroup of GL(n). The key ingredients of the construction are the longest element of the Weyl group, the quantum dilogarithm function, and central elements of the quantized division algebra of rational functions on the subgroup in question.

Mathematics Subject Classification

20G42 16K20 16T25 

Keywords

tetrahedron equation quantum dilogarithm quantum group 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Section of MathematicsUniversity of GenevaGeneva 4Switzerland
  2. 2.Steklov Mathematical InstituteRussian Academy of SciencesSt. PetersburgRussia

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