# Question on the form of a vertex operator in a proof

by Schure
Tags: cft, representation, vertex operator, virasoro
 P: 1 Ok, never mind - I decided to find the solution in a different way.. This is a little too specialized anyway. (Is there a way to delete the thread?) Hi, I am reading paper [1] and I found that formula (33), $$\psi(xy)\psi^*(y)=\frac 1{x^{1/2}-x^{-1/2}}\exp\left(\sum_n\frac{(xy)^n-y^n}{n}\alpha_{-n}\right)\exp\left(\sum_n\frac{y^{-n}-(xy)^{-n}}n\alpha_n\right)$$ is almost in accordance to its alleged source [2, Theorem 14.10], except for the factor at the front, namely, $$\frac1{x^{1/2}-x^{-1/2}}.$$ Does anyone know where that comes from? Probably this comes from the shift of coordinates that happens when Eskin and Okounkov use half-integers for the indices in the infinite wedge representation, instead of the usual whole integers. But I have not found the way to fully justify the term using this. I'd really appreciate a hint! Thanks! Schure [1] A. Eskin and A. Okounkov, Pillowcases and quasimodular forms, http://arxiv.org/pdf/math/0505545.pdf [2] Kac, Infinite dimensional Lie algebras, 3rd edition
 Sci Advisor HW Helper P: 1,320 Do stick around Schure, it's good to have some specialized discussion now and again. I find it a nice change of pace from the nth iteration of interpreting quantum mechanics, the twin paradox, or "is string theory science?" There are some very knowledgeable people who hang out here.

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