On deformed W-algebras and quantum affine algebras

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.

40 pages, plain TeX with amssym.def, improved referencing

References in corpus (7)

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Cited by in corpus (3)

• Langlands duality for finite-dimensional representations of quantum affine algebras
• Singular Vector of Ding-Iohara-Miki Algebra and Hall-Littlewood Limit of 5D AGT Conjecture
• Quantum affine Toda solitons