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Generalized imaginary Verma and Wakimoto modules
Institution:1. Institute of Mathematics, University of São Paulo, Caixa Postal 66281, CEP 05314-970, São Paulo, Brazil;2. Universidade Federal de Amazonas, 2089, R. Nossa Sra. do Rosário, 1951, CEP 69100-000, Itacoatiara, Brazil;1. School of Mathematics and Statistics, Northwestern Polytechnical University, Xi''an, Shaanxi 710072, PR China;2. Department of Mathematics, University of Wisconsin-Whitewater, 800 W. Main Street, Whitewater, WI 53190, USA;3. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, PR China;4. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, PR China;1. Department of Mathematics, Free University of Brussels, 1050 Brussels, Belgium;2. Department of Mathematics, ORT Braude College, 2161002 Karmiel, Israel;1. Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146 Genova, Italy;2. Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487, USA;3. Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA;1. Department of Mathematics, Southwest Jiaotong University, Sichuan 611756, China;2. Department of Mathematics, University of Virginia, Charlottesville, VA 22904, USA;1. Department of Mathematics, Southwest Jiaotong University, Chengdu 610031, PR China;2. Department of Mathematics, Sichuan University, Chengdu 610064, PR China;3. Department of Mathematics, University of Virginia, Charlottesville, VA 22904, United States of America
Abstract:We develop a general technique of constructing new irreducible weight modules for any affine Kac-Moody algebra using the parabolic induction, in the case when the Levi factor of a parabolic subalgebra is infinite-dimensional and the central charge is nonzero. Our approach unifies and generalizes all previously known results with imposed restrictions on inducing modules. We also define generalized imaginary Wakimoto modules which provide an explicit realization for generic generalized imaginary Verma modules.
Keywords:Affine Kac–Moody algebra  Wakimoto module  Twisting functor  Imaginary Verma module
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