Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 317-331 |
| Number of pages | 15 |
| Journal | Nuclear Physics B |
| Volume | 277 |
| Issue number | C |
| DOIs | |
| State | Published - 1986 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Nuclear and High Energy Physics
Cite this
Vertex operator construction of the SO(2n+1) Kac-Moody algebra and its spinor representation. / Alvarez, Orlando; Windey, Paul; Mangano, Michelangelo.
In: Nuclear Physics B, Vol. 277, No. C, 1986, p. 317-331.Research output: Contribution to journal › Article
}
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
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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UR - http://www.scopus.com/inward/citedby.url?scp=24544466811&partnerID=8YFLogxK
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 -