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Multivariable Appell functions and nonholomorphic Jacobi forms

Multivariable Appell functions and nonholomorphic Jacobi forms Multivariable Appell functions show up in the work of Kac and Wakimoto in the computation of character formulas for certain $$s \ell (m,1)^\wedge $$ s ℓ ( m , 1 ) ∧ modules. Bringmann and Ono showed that the character formulas for the $$s \ell (m,1)^\wedge $$ s ℓ ( m , 1 ) ∧ modules $$L(\varLambda _{(s)})$$ L ( Λ ( s ) ) , where $$L(\varLambda _{(s)})$$ L ( Λ ( s ) ) is the irreducible $$s \ell (m,1)^\wedge $$ s ℓ ( m , 1 ) ∧ module with the highest weight $$\varLambda _{(s)}$$ Λ ( s ) , can be seen as the “holomorphic parts” of certain nonholomorphic modular functions. Here, we consider more general multivariable Appell functions and relate them to nonholomorphic Jacobi forms. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Research in the Mathematical Sciences Springer Journals

Multivariable Appell functions and nonholomorphic Jacobi forms

Research in the Mathematical Sciences , Volume 6 (1) – Jan 24, 2019

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Publisher
Springer Journals
Copyright
Copyright © 2019 by Springer Nature Switzerland AG
Subject
Mathematics; Mathematics, general; Applications of Mathematics; Computational Mathematics and Numerical Analysis
eISSN
2197-9847
DOI
10.1007/s40687-019-0178-0
Publisher site
See Article on Publisher Site

Abstract

Multivariable Appell functions show up in the work of Kac and Wakimoto in the computation of character formulas for certain $$s \ell (m,1)^\wedge $$ s ℓ ( m , 1 ) ∧ modules. Bringmann and Ono showed that the character formulas for the $$s \ell (m,1)^\wedge $$ s ℓ ( m , 1 ) ∧ modules $$L(\varLambda _{(s)})$$ L ( Λ ( s ) ) , where $$L(\varLambda _{(s)})$$ L ( Λ ( s ) ) is the irreducible $$s \ell (m,1)^\wedge $$ s ℓ ( m , 1 ) ∧ module with the highest weight $$\varLambda _{(s)}$$ Λ ( s ) , can be seen as the “holomorphic parts” of certain nonholomorphic modular functions. Here, we consider more general multivariable Appell functions and relate them to nonholomorphic Jacobi forms.

Journal

Research in the Mathematical SciencesSpringer Journals

Published: Jan 24, 2019

References