A note on decoupling conditions for generic level (sl)over-cap(3)(k) and fusion rules

TY - JOUR

T1 - A note on decoupling conditions for generic level (sl)over-cap(3)(k) and fusion rules

AU - Ganchev, A C

AU - Petkova, V B

AU - Watts, G M T

PY - 2000

Y1 - 2000

N2 - We find the solution of the (3)(k) singular vector decoupling equations on 3-point functions for the particular case when one of the fields is of weight w(0) . k Lambda(0). The result is a function with non-trivial singularities in the flag variables, namely a linear combination of F-2(1) hypergeometric functions. This calculation fills in a gap in [Nucl, Phys, B 518 (1998) 645; Commun. Math. Phys, 202 (1999) 701]. and confirms the (3)(k) fusion rules determined there both for generic kappa is not an element of Q and fractional levels. We have also analysed the fusion in (3)(k) using algebraic methods generalising those of Feigin and Fuchs and again find agreement with [Nucl. Phys. B 518(1998) 635; Commun. Math. Phys. 202 (1999) 701], In the process we clarify some details of previous treatments of the fusion of (2)(k) fractional level admissible representations. (C) 2000 Elsevier Science B.V. All rights reserved.

AB - We find the solution of the (3)(k) singular vector decoupling equations on 3-point functions for the particular case when one of the fields is of weight w(0) . k Lambda(0). The result is a function with non-trivial singularities in the flag variables, namely a linear combination of F-2(1) hypergeometric functions. This calculation fills in a gap in [Nucl, Phys, B 518 (1998) 645; Commun. Math. Phys, 202 (1999) 701]. and confirms the (3)(k) fusion rules determined there both for generic kappa is not an element of Q and fractional levels. We have also analysed the fusion in (3)(k) using algebraic methods generalising those of Feigin and Fuchs and again find agreement with [Nucl. Phys. B 518(1998) 635; Commun. Math. Phys. 202 (1999) 701], In the process we clarify some details of previous treatments of the fusion of (2)(k) fractional level admissible representations. (C) 2000 Elsevier Science B.V. All rights reserved.

U2 - 10.1016/S0550-3213(99)00745-2

DO - 10.1016/S0550-3213(99)00745-2

M3 - Article

VL - 571

SP - 457

EP - 478

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 1-2

ER -