Contributions à l'Etude du Vertex Topologique en Théorie ... - Toubkal

013509-6 Drissi, Jehjouh, and Saidi J. Math. Phys. 50, 013509 2009The vertex operators z are given by = q−/2+n−/2+nt 2 l+l . 3.13 + z = exp mNodd2m zm m, − z = exp mNodd2m zm −m,3.14with m being operators satisfying the following commutation relations: m , n =− m 2 n+m,0, m, n Z odd . 3.15Notice that in the particular limit N 1 , N 2 , and N 3 →, the vertex S gets identified withS 3 q =shifted 3d 2 p q , 3.16whose explicit expression is precisely 2.9.Step 2: Commuting the vertex operators + z i to the right of − z j by using the commutationrelations + x − y = 1+xy1−xy − y + x, x y = y x,3.17we getS = strict 2d t N 1 N 2 − q − t j− j + q − i − i,j=1i=13.18with =Z q−/2+n−/2+nt 2 l+l . 3.19This relation can be simplified further by using the Schur functions P t /x j = t − x j andQ t /x i = t + x j following from the identities t N 2 j=1 − x j = P / x 1 ,...,x N , t N 1 j=1 = x j =Q / x 1 ,...,x N , as well asDownloaded 24 Mar 2009 to 140.105.16.64. Redistribution subject to AIP license or copyright; see http://jmp.aip.org/jmp/copyright.jsp