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By Rockswold G. K.

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Proof. , X/]]. j = l n>0 n The coefficients in the formal power series A and B span, respectively, M ( l ) z ® ^(a) and M ( l ) z ® t(b). It is, therefore, sufficient to prove the theorem with u and v replaced, respectively, by A and B (cf. [6], pp. 205-6). n(a,,z + ti;it)° II iz-<5^>. )" • The next step of the proof will be to compute exp(Az*)A, and Y+(A, z) (cf. 48)). --Yz(ak,wk)t(l) JJ l.

17) as in Section 2 (cf. 21)). 2). 14), where {e a , a £ l } denotes the usual basis of the group algebra C[L] with multiplication given by e a e^ = e a+/? , a,/? G L and where l z + i ( v , 2), v £ VL, denotes the (general) twisted vertex operator defined in [6], Chapter 9. 20) (cf. 9)). 19) can be applied to a single |ct t , for each i G {1,2, • • •, k}. 23) determined by TT,(C) = 1, *i(d) = tjf, *i(a tp) = cti ® i p , peZ *i{*±a{z)) = Y£lk{eka\z). 19). 22), the action of Y^+i (e ±a », z) on V% coincides with the action of 1 ® • • • ® 1 ® Y^\(e±a\z) ® 1 ® • • • ® 1, where the nontrivial tensorand is in the imposition.

49) (cf. 50) t; K-> Y0+(v,z). 17), we define Y °-^ =: ((^ri)i(£»n'-,aiw) ((^bji(|)"^w) 1 ' (njfe — r (^r-v 4 (zA K(«,^);. 1)! 52) v H-* Y0*(v,z). 54) v i—• Ym(vjz). (^,^o)i(6),^) = n-l =° exp f £ ^ ( ^ ) S'(*aKJ n((tfa)6,zj,)2. 56) CRISTIANO 38 HUSU Note that 2 <-a>fi>>-<-a>,l>> / (1 + * ) 1 + 1 = z^^z^^ [(1 + y ^ 24. 58) is the relative Z2-twisted Jacobi identity for the vectors u = t(a) and v = i(b). 1 (the relative Z2-twisted Jacobi identity) Let a, b G L, and let r,s e M(l)z; set u = r ® t(a), v = s ® ^(6), (u,t; 6 VL), (C/.

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A0-stable linear multistep formulas of the-type by Rockswold G. K.


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