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Extra info for Communications in Mathematical Physics - Volume 212
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J. Mod. Phys. A 9, 399–417 (1994) 3. : Difference equations with elliptic coefficients and quantum affine algebras. hep-th/9312057 4. Frenkel, I. , Vertex representations of quantum affine algebras. Proc. Natl. Acad. Sci. USA 85, 9373–9377 (1988) 5. : Basic representations of affine Lie algebras and dual resonance models. Invent. Math. 62, 23–66 (1980) 6. Frenkel, I. : Quantum affine algebras and holonomic difference equations. Commun. Math. Phys. 146, 1–60 (1992) 7. Hong, J. , Miwa, T. : Vertex models with alternating spins.
Derivation of Integral Formula for Trace The calculation of the trace using the bosonic expression of the intertwining operators are similar to the case of N = 2 [9, 8]. Thus we simply present the necessary information for the calculation of the trace. 58 A. Nakayashiki We use the following formula: trV ( N−1 ∞ x D exp i) N −1 ∞ (j ) j =1 n=1 N−1 −∂ ¯ cj αj )g0 × exp( (j ) An aj (−n) exp j =1 1 Bn aj (n) j =1 n=1 −∂ ¯ gN N −1 N −1 ∂α j gj j =1 −( ¯ 1 | ¯ i ) −( ¯ N −1 | ¯ i ) 1−δi0 −1 −1 N 2 gN gi θi (g0−1 g12 g2−1 , · · · , gN = (x N )−1 ∞ g0 −2 gN −1 gN |x ) N−1 ∞ ∞ 1 Nmn (j ) (j −1) (j ) (j +1) exp An (−[n]2 Bn + [n][2n]Bn − [n]2 Bn ) x × n m=1 n=1 j =1 , (34) (0) (N ) where we set Bn = Bn = 0.
Hence the matrix D(ζ |ζ |1)M,L M,L is a diagonal matrix and det D(ζ |ζ |1)M,L M,L This completes the proof. D(ζ |ζ |1)M,M = N P = M (za − zb )2 . M r