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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.
Research in the Mathematical Sciences – Springer Journals
Published: Jan 24, 2019
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