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On deformed W-algebras and quantum affine algebras

P. Bouwknegt·K. Pilch
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Abstract

We discuss some aspects of the deformed W-algebras W_{q,t}[g]. In particular, we derive an explicit formula for the Kac determinant, and discuss the center when t^2 is a primitive k-th root of unity. The relation of the structure of W_{q,t}[g] to the representation ring of the quantum affine algebra U_q(\hat g), as discovered recently by Frenkel and Reshetikhin, is further elucidated in some examples.

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P. Bouwknegt, K. Pilch. 1998-02-19. On deformed W-algebras and quantum affine algebras. https://arxiv.org/abs/math/9801112

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