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We present a new expression for the partition function of the refined Chern-Simons theory on S3 with an arbitrary gauge group, which is explicitly equal to 1 when the coupling constant is zero. Using this form of the partition function we show that the previously known Krefl-Schwarz representation of the partition function of the refined Chern-Simons theory on S3 can be generalized to all simply laced algebras. For all non-simply laced gauge algebras, we derive similar representations of that partition function, which makes it possible to transform it into a product of multiple sine functions aiming at the further establishment of duality with the refined topological strings. [ABSTRACT FROM AUTHOR]

We present a new expression for the partition function of the refined Chern-Simons theory on S3 with an arbitrary gauge group, which is explicitly equal to 1 when the coupling constant is zero. Using this form of the partition function we show that the previously known Krefl-Schwarz representation of the partition function of the refined Chern-Simons theory on S3 can be generalized to all simply laced algebras. For all non-simply laced gauge algebras, we derive similar representations of that partition function, which makes it possible to transform it into a product of multiple sine functions aiming at the further establishment of duality with the refined topological strings. [ABSTRACT FROM AUTHOR]