v 1 2 4 A pr 1 99 5 A Link Invariant from Quantum Dilogarithm
The link invariant, arising from the cyclic quantum dilogarithm via the particular R-matrix construction, is proved to coincide with the invariant of triangulated links in S introduced in [14]. The obtained invariant, like Alexander-Conway polynomial, vanishes on disjoint union of links. The R-matrix can be considered as the cyclic analog of the universal R-matrix associated with Uq(sl(2)) algebra.
Remarks on the quantum dilogarithm
A quantum analogue of the dilogarithm function has been introduced by Faddeev and Kashaev (1994) in such a way that a certain identity in the Weyl algebra Wq, plays the role of the five-term dilogarithm identity. We study this identity in the limit when q approaches a root of unity and show that it then reduces to the 'restricted star-triangle relation' which has been used previously by Bazhanov and Baxter (1992) as a local integrability condition of a class of three-dimensional solvable lattice models.
Fermionic quasi-particle representations for characters of (G (1) ) 1 × (G (1) ) 1 /(G (1) ) 2
Abstract We present fermionic quasi-particle sum representations for some of the characters (or branching functions) of ( G (1) ) 1 × ( G (1) ) 1 ( G (1) ) 2 for all simply-laced Lie algebras G. For given G the charactters are written as the partition function of a set of rank G types of massless quasi-particles in certain charge sectors, with nontrivial lower bounds on the one-particle momenta. We discuss the non-uniqueness of the representation for the identity character of the critical Ising model, which arises in both the A 1 and E 8 cases.