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Multiplicity formulas for a class of representations of affine Kac-Moody algebras. (English) Zbl 0791.17027

Summary: The dominant weight of any highest weight irreducible representation (irrep) of an indecomposable affine algebra may be written in the form \(\Lambda_ i-q \delta\), where the integral index \(i\) runs from 1 to some finite number (called the width of the representation), \(q\) is any nonnegative integer, and \(\delta\) is a vector called the null vector. All the width-two irreps of all the affine algebras are enumerated. Techniques used in an earlier paper on the width-one irreps [the first author, J. Phys. A, Math. Gen. 23, 4727-4738 (1990; Zbl 0725.17028)] are generalized and used to compute simple recursion formulas for the multiplicities of all these dominant weights. These formulas are suitable for rapid calculations. Numerical tables of the multiplicities of the highest 33 dominant weights are given for all the width-two irreps of twisted algebras.

MSC:

17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
17-04 Software, source code, etc. for problems pertaining to nonassociative rings and algebras

Citations:

Zbl 0725.17028
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