Macdonald Identities, Weyl-Kac Denominator Formulas and Affine Grassmannian Elements

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2025
• ISSN: 1815-0659
• Main Authors: Lecouvey, Cédric, Wahiche, David
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2025
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/213190
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Macdonald Identities, Weyl-Kac Denominator Formulas and Affine Grassmannian Elements. Cédric Lecouvey and David Wahiche. SIGMA 21 (2025), 023, 45 pages

The Nekrasov-Okounkov formula gives an expression for the Fourier coefficients of the Euler functions as a sum of hook length products. This formula can be deduced from a specialization in a renormalization of the affine type Weyl denominator formula and the use of a polynomial argument. In this pa...