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The Dedekind eta function and D’Arcais-type polynomials

The Dedekind eta function and D’Arcais-type polynomials D’Arcais-type polynomials encode growth and non-vanishing properties of the coefficients of powers of the Dedekind eta function. They also include associated Laguerre polynomials. We prove growth conditions and apply them to the representation theory of complex simple Lie algebras and to the theory of partitions, in the direction of the Nekrasov–Okounkov hook length formula. We generalize and extend results of Kostant and Han. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Research in the Mathematical Sciences Springer Journals

The Dedekind eta function and D’Arcais-type polynomials

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References (24)

Publisher
Springer Journals
Copyright
Copyright © Springer Nature Switzerland AG 2020
eISSN
2197-9847
DOI
10.1007/s40687-019-0201-5
Publisher site
See Article on Publisher Site

Abstract

D’Arcais-type polynomials encode growth and non-vanishing properties of the coefficients of powers of the Dedekind eta function. They also include associated Laguerre polynomials. We prove growth conditions and apply them to the representation theory of complex simple Lie algebras and to the theory of partitions, in the direction of the Nekrasov–Okounkov hook length formula. We generalize and extend results of Kostant and Han.

Journal

Research in the Mathematical SciencesSpringer Journals

Published: Jan 16, 2020

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