2004/01/31 by L. Feher, I. Marshall
Mathematics · Physics and Astronomy · #math.QA #hep-th #math-ph #math.MP #math.SG #msc:37J15 #msc:53D17 #msc:17Bxx #msc:81T40
published as Int. Math. Res. Not. 2004, no. 49, 2611-2636 · 22 pages, v2: with clarifying remarks added in the introduction
arxiv created 2004/04/05 · arxiv updated 2009/12/01
The gauge action of the Lie group G on the chiral WZNW phase space \cal M\check G of quasiperiodic fields with \check G-valued monodromy, where \check G⊂ G is an open submanifold, is known to be a Poisson-Lie (PL) action with respect to any coboundary PL structure on G, if the Poisson bracket on \cal M\check G is defined by a suitable monodromy dependent exchange r-matrix. We describe the momentum map for these symmetries when G is either a factorisable PL group or a compact simple Lie group with its standard PL structure. The main result is an explicit one-to-one correspondence between the monodromy variable M ∈ \check G and a conventional variable Ω∈ G^*. This permits us to convert the PL groupoid associated with a WZNW exchange r-matrix into a `canonical' PL groupoid constructed from the Heisenberg double of G, and consequently to obtain a natural PL generalization of the classical dynamical Yang-Baxter equation.