312 research outputs found
String Functions for Affine Lie Algebras Integrable Modules
The recursion relations of branching coefficients for a
module reduced to a Cartan subalgebra
are transformed in order to place the recursion shifts into the fundamental Weyl chamber. The new
ensembles (the "folded fans") of shifts were constructed and the
corresponding recursion properties for the weights belonging to the fundamental
Weyl chamber were formulated. Being considered simultaneously for the set of
string functions (corresponding to the same congruence class of
modules) the system of recursion relations constitute an equation
where
the operator is an invertible matrix whose
elements are defined by the coordinates and multiplicities of the shift weights
in the folded fans and the components of the vector
are the string function coefficients for
enlisted up to an arbitrary fixed grade . The examples are presented where
the string functions for modules of are explicitly
constructed demonstrating that the set of folded fans provides a compact and
effective tool to study the integrable highest weight modules.Comment: This is a contribution to the Special Issue on Kac-Moody Algebras and
Applications, published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
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