(adsbygoogle = window.adsbygoogle || []).push({}); [Closed] Question on the form of a vertex operator in a proof

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?)

[STRIKE]Hi,

I am reading paper [1] and I found that formula (33),

[tex]\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)[/tex]

is almost in accordance to its alleged source [2, Theorem 14.10], except for the factor at the front, namely,

[tex]\frac1{x^{1/2}-x^{-1/2}}.[/tex]

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[/STRIKE]

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

**Physics Forums | Science Articles, Homework Help, Discussion**