# Wakimoto realizations of current algebras: an explicit construction

### Description

A generalized Wakimoto realization of $\widehat\cal G_K$ can be associated with each parabolic subalgebra $\cal P=(\cal G_0 +\cal G_+)$ of a simple Lie algebra $\cal G$ according to an earlier proposal by Feigin and Frenkel. In this paper the proposal is made explicit by developing the construction of Wakimoto realizations from a simple but unconventional viewpoint. An explicit formula is derived for the Wakimoto current first at the Poisson bracket level by Hamiltonian symmetry reduction of the WZNW model. The quantization is then performed by normal ordering the classical formula and determining the required quantum correction for it to generate ... continued below

### Creation Information

de Boer, Jan & Feher, Laszlo November 12, 1996.

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## What

### Description

A generalized Wakimoto realization of $\widehat\cal G_K$ can be associated with each parabolic subalgebra $\cal P=(\cal G_0 +\cal G_+)$ of a simple Lie algebra $\cal G$ according to an earlier proposal by Feigin and Frenkel. In this paper the proposal is made explicit by developing the construction of Wakimoto realizations from a simple but unconventional viewpoint. An explicit formula is derived for the Wakimoto current first at the Poisson bracket level by Hamiltonian symmetry reduction of the WZNW model. The quantization is then performed by normal ordering the classical formula and determining the required quantum correction for it to generate $\widehat\cal G_K$ by means of commutators. The affine-Sugawara stress-energy tensor is verified to have the expected quadratic form in the constituents, which are symplectic bosons belonging to $\cal G_+$ and a current belonging to $\cal G_0$. The quantization requires a choice of special polynomial coordinates on the big cell of the flag manifold $P\backslash G$. The effect of this choice is investigated in detail by constructing quantum coordinate transformations. Finally, the explicit form of the screening charges for each generalized Wakimoto realization is determined, and some applications are briefly discussed.

### Source

• Journal Name: Communications in Mathematical Physics; Related Information: Journal Publication Date: 11/01/1997

### Identifier

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• Report No.: LBNL-39562
• Grant Number: DE-AC02-05CH11231
• Office of Scientific & Technical Information Report Number: 965357

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## When

### Creation Date

• November 12, 1996

### Added to The UNT Digital Library

• Nov. 13, 2016, 7:26 p.m.

### Description Last Updated

• Nov. 18, 2016, 3:36 p.m.

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