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Double affine Hecke algebra in logarithmic conformal field theory. (English. Russian original) Zbl 1271.81155
Funct. Anal. Appl. 44, No. 1, 55-64 (2010); translation from Funkts. Anal. Prilozh. 44, No. 1, 68-79 (2010).
Summary: We construct a representation of the double affine Hecke algebra. The symmetrization of this representation coincides with the center of the quantum group \(\overline{\mathcal U}_{\mathfrak q}s\ell(2)\) and, by Kazhdan-Lusztig duality with the Verlinde algebra of the \((1,p)\)-model of the logarithmic conformal field theory.

MSC:
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
20C08 Hecke algebras and their representations
17B37 Quantum groups (quantized enveloping algebras) and related deformations
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