An Elliptic Algebra U q,p ( s l 2 ^ ) and the Fusion RSOS Model
Abstract
We introduce an elliptic algebra
U
q,p
(
s
l
2
^
)
with $p=q^{2r} (r\in \R_{>0})$ and present its free boson representation at generic level
k
. We show that this algebra governs a structure of the space of states in the
k−
fusion RSOS model specified by a pair of positive integers
(r,k)
, or equivalently a
q−
deformation of the coset conformal field theory
SU(2
)
k
×SU(2
)
r−k−2
/SU(2
)
r−2
. Extending the work by Lukyanov and Pugai corresponding to the case
k=1
, we gives a full set of screening operators for
k>1
. The algebra
U
q,p
(
s
l
2
^
)
has two interesting degeneration limits,
p→0
and
p→1
. The former limit yields the quantum affine algebra
U
q
(
s
l
2
^
)
whereas the latter yields the algebra
A
ℏ,η
(
s
l
2
^
)
, the scaling limit of the elliptic algebra
A
q,p
(
s
l
2
^
)
. Using this correspondence, we also obtain the highest component of two types of vertex operators which can be regarded as
q−
deformations of the primary fields in the coset conformal field theory.