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Rademacher-type formulas for the multiplicities of irreducible highest-weight representations of affine Lie algebras
| Content Provider | Semantic Scholar |
|---|---|
| Author | Moreno, Carlos J. Rocha-Caridi, Alvany |
| Copyright Year | 1987 |
| Abstract | The weight lattice of an integrable irreducible highest-weight representation of an affine Lie algebra is a union of infinite strings. Furthermore, the multiplicities in a finite number of strings determine all the multiplicities. Kac and Peterson [1, 2] have shown that the multiplicities in the same string are the Fourier coefficients of a modular form of negative weight, called a string function. This result, together with combinatorial identities for the Dedekind ?/-function, was successfully used in [1 and 2] to determine the string functions in many interesting cases. In this paper, we make use of the result of [1 and 2] to adapt Rademacher's circle method to the string functions and derive formulas for their coefficients. The formulas obtained are of the type proved by Rademacher in [3] for the partition function. This new approach opens the way towards an explicit determination of the Fourier coefficients which goes beyond the combinatorial method. As an example, we show how to calculate the coefficients in the case of the affine Lie algebra of type C± ', which is the simplest nontrivial case not treated in [1 and 2]. |
| Starting Page | 292 |
| Ending Page | 296 |
| Page Count | 5 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0273-0979-1987-15520-0 |
| Alternate Webpage(s) | http://www.ams.org/journals/bull/1987-16-02/S0273-0979-1987-15520-0/S0273-0979-1987-15520-0.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0273-0979-1987-15520-0 |
| Volume Number | 16 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
