### Abstract

A generalized Wakimoto realization of Ĝ_{K} can be associated with each parabolic subalgebra P = (G_{0} + G_{+}) of a simple Lie algebra 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 Ĝ_{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 G_{+} and a current belonging to G_{0}. The quantization requires a choice of special polynomial coordinates on the big cell of the flag manifold P\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.

Original language | English |
---|---|

Pages (from-to) | 759-793 |

Number of pages | 35 |

Journal | Communications in Mathematical Physics |

Volume | 189 |

Issue number | 3 |

Publication status | Published - 1997 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

*Communications in Mathematical Physics*,

*189*(3), 759-793.

**Wakimoto realizations of current algebras : An explicit construction.** / De Boer, Jan; Fehér, L.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 189, no. 3, pp. 759-793.

}

TY - JOUR

T1 - Wakimoto realizations of current algebras

T2 - An explicit construction

AU - De Boer, Jan

AU - Fehér, L.

PY - 1997

Y1 - 1997

N2 - A generalized Wakimoto realization of ĜK can be associated with each parabolic subalgebra P = (G0 + G+) of a simple Lie algebra 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 ĜK 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 G+ and a current belonging to G0. The quantization requires a choice of special polynomial coordinates on the big cell of the flag manifold P\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.

AB - A generalized Wakimoto realization of ĜK can be associated with each parabolic subalgebra P = (G0 + G+) of a simple Lie algebra 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 ĜK 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 G+ and a current belonging to G0. The quantization requires a choice of special polynomial coordinates on the big cell of the flag manifold P\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.

UR - http://www.scopus.com/inward/record.url?scp=0031549889&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031549889&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031549889

VL - 189

SP - 759

EP - 793

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -