TY - JOUR

T1 - Vertex operator construction of the SO(2n+1) Kac-Moody algebra and its spinor representation

AU - Alvarez, Orlando

AU - Windey, Paul

AU - Mangano, Michelangelo

N1 - Funding Information:
1 Alfred P. Sloan Foundation fellow. 2 This work was supported by the National Science Foundation under grant PHY-81-18547. 3 This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the US Department of Energy under Contracts DE-AC03-76SF00098. 4 Supported by an INFN Fellowship. * A Lie algebra is said to be simply laced if all the roots have the same length.

PY - 1986

Y1 - 1986

N2 - An explicit representation of the Bn(1) affine Lie algebra (Kac-Moody algebra) is constructed in terms of vertex operators associated with the Chevalley basis of the underlyingfinite-dimentsionnal Lie algebra. This construction, contrary to the simpler current algebra one, gives a concrete realization of the spinor representation of the algebra. The key feature is a partial bosonization of two-dimensional Weyl-Majorana free fermions. The vertex operators associated with the long and short roots of the Bn algebra have fermion number zero and one, respectively.

AB - An explicit representation of the Bn(1) affine Lie algebra (Kac-Moody algebra) is constructed in terms of vertex operators associated with the Chevalley basis of the underlyingfinite-dimentsionnal Lie algebra. This construction, contrary to the simpler current algebra one, gives a concrete realization of the spinor representation of the algebra. The key feature is a partial bosonization of two-dimensional Weyl-Majorana free fermions. The vertex operators associated with the long and short roots of the Bn algebra have fermion number zero and one, respectively.

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U2 - 10.1016/0550-3213(86)90444-X

DO - 10.1016/0550-3213(86)90444-X

M3 - Article

AN - SCOPUS:24544466811

VL - 277

SP - 317

EP - 331

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - C

ER -