Collective hamiltonians with Kac-Moody algebraic conditions |
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| Institution: | 1. School of Mathematics, South China University of Technology, Guangzhou 510640, China;2. Pazhou Lab, Guangzhou 510330, China;3. International Research Center for Neurointelligence, The University of Tokyo, Tokyo 113-8654, Japan;4. Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan;5. State Key Laboratory of Cell Biology, Shanghai Institute of Biochemistry and Cell Biology, Center for Excellence in Molecular Cell Science, Chinese Academy of Sciences, Shanghai 200031, China;6. Center for Excellence in Animal Evolution and Genetics, Chinese Academy of Sciences, Kunming 650223, China;7. Key Laboratory of Systems Health Science of Zhejiang Province, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences, Chinese Academy of Sciences, Hangzhou 310024, China;1. School of Atmospheric Sciences, Nanjing University, Nanjing, 210023, China;2. Department of Geography and Planning, University of Toronto, Toronto, M5S 3G3, Canada;3. Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Key Laboratory for Aerosol-Cloud-Precipitation of China Meteorological Administration, Nanjing University of Information Science & Technology, Nanjing, 210044, China;4. International Institute for Earth System Science, Nanjing University, Nanjing, 210023, China;1. Department of Computer Engineering, Afarinesh Institute of Higher Education, Boroujerd, Iran;2. Department of Electrical, Computer and Biomedical Engineering, Islamic Azad University, Qazvin, Iran;3. Department of Electrical, Computer and Biomedical Engineering, Islamic Azad University, Qazvin, Iran;1. Groningen University, Department of Education, Faculty of Behavioral and Social Sciences, Grote Rozenstraat 38, 9712 TJ Groningen, The Netherlands;2. University of Amsterdam, Department of Social Psychology, Weesperplein 4, 1018 XA Amsterdam, The Netherlands;3. VU University Amsterdam, Department of Theory and Research in Education, Faculty of Psychology & Education, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands;1. Department of Public Finance, University of Innsbruck, Austria;2. Technical University of Munich, School of Management, Department of Economics & Policy, Germany;3. Center for the Economics of Education, ifo Institute Munich, and CESifo, Germany;4. Max Planck Institute for Research on Collective Goods, Germany;5. University of Cologne, Germany;6. University of Innsbruck, Austria;7. IZA Bonn, Germany;1. Intelligent Computing and Machine Learning Lab, School of Automation Science and Electrical Engineering, Beihang University, Beijing, China;2. Department of Computer Science and Engineering, Hong Kong University of Science and Technology, Hong Kong, China;3. Department of Biological Science and Medical Engineering, Beihang University, China |
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| Abstract: | We describe the general framework for constructing collective-theory hamiltonians whose hermiticity requirements imply a Kac-Moody algebra of constraints on the associated jacobian. We give explicit examples for the algebras sl(2)k and sl(3)k. The reduction to Wn-constraints, relevant to n-matrix models, is described for the jacobians. |
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