Algebraic Structures and Correlations in Quantum Many-Body Systems

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Algebraic structures such as quantized superalgebras are among the most important discoveries in mathematics and have applications in a wide range of physics. Internationally there has been recent excitement about vertex operators and representations of these algebraic structures and their applications to integrable systems and quantum field theory. I have made significant contributions to this rapidly expanding field, and will capitalize on this success. I will develop a comprehensive theory of these mathematical structures and their applications in the construction of correlation functions and form factors, and in so doing write a definitive monograph on the subject.