Free boson realization of U-q(sl(N)

Awata, Hidetoshi; Odake, Satoru; Shiraishi, Junichi

doi:10.1007/BF02105187

Free boson realization of U-q(sl(N)

May, 1993

24 pages

Published in:

Commun.Math.Phys. 162 (1994) 61-84

e-Print:

hep-th/9305146 [hep-th]

DOI:

10.1007/BF02105187

Report number:

RIMS-924,
YITP-K-1018

View in:

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Abstract:

We construct a realization of the quantum affine algebra

U_q(\widehat{sl_N})

of an arbitrary level

k

in terms of free boson fields. In the

q\!\rightarrow\! 1

limit this realization becomes the Wakimoto realization of

\widehat{sl_N}

. The screening currents and the vertex operators(primary fields) are also constructed; the former commutes with

U_q(\widehat{sl_N})

modulo total difference, and the latter creates the

U_q(\widehat{sl_N})

highest weight state from the vacuum state of the boson Fock space.

Note:

24 pages, LaTeX, RIMS-924, YITP/K-1018

quantum algebra: SL(N)
quantum algebra: representation
current: screening
operator: vertex
operator product expansion

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