A-D-E Polynomial and Rogers--Ramanujan Identities

Details A-D-E Polynomial and Rogers--Ramanujan Identities A-D-E Polynomial and Rogers--Ramanujan Identities

1994-11-02

arxiv.org/abs/hep-th/9411009v1

Int. J. Mod. Phys. A11 (1996) 291

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, Latex, 1 Postscript figure

Scientific paper

10.1142/S0217751X96000146

We conjecture polynomial identities which imply Rogers--Ramanujan type identities for branching functions associated with the cosets $({\cal G}^{(1)})_{\ell-1}\otimes ({\cal G}^{(1)})_{1} / ({\cal G}^{(1)})_{\ell}$, with ${\cal G}$=A$_{n-1}$ \mbox{$(\ell\geq 2)$}, D$_{n-1}$ $(\ell\geq 2)$, E$_{6,7,8}$ $(\ell=2)$. In support of our conjectures we establish the correct behaviour under level-rank duality for $\cal G$=A$_{n-1}$ and show that the A-D-E Rogers--Ramanujan identities have the expected $q\to 1^{-}$ asymptotics in terms of dilogarithm identities. Possible generalizations to arbitrary cosets are also discussed briefly.

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