Communications in Mathematical Physics

, Volume 264, Issue 2, pp 427–464

Fermionic Characters and Arbitrary Highest-Weight Integrable Open image in new window-Modules

Article

DOI: 10.1007/s00220-005-1486-3

Cite this article as:
Ardonne, E., Kedem, R. & Stone, M. Commun. Math. Phys. (2006) 264: 427. doi:10.1007/s00220-005-1486-3

Abstract

This paper contains the generalization of the Feigin-Stoyanovsky construction to all integrable Open image in new window-modules. We give formulas for the q-characters of any highest-weight integrable module of Open image in new window as a linear combination of the fermionic q-characters of the fusion products of a special set of integrable modules. The coefficients in the sum are the entries of the inverse matrix of generalized Kostka polynomials in q−1. We prove the conjecture of Feigin and Loktev regarding the q-multiplicities of irreducible modules in the graded tensor product of rectangular highest weight-modules in the case of Open image in new window. We also give the fermionic formulas for the q-characters of the (non-level-restricted) fusion products of rectangular highest-weight integrable Open image in new window-modules.

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of IllinoisUrbanaUSA
  2. 2.Department of MathematicsUniversity of IllinoisUrbanaUSA