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Titlebook: Elliptic Quantum Groups; Representations and Hitoshi Konno Book 2020 Springer Nature Singapore Pte Ltd. 2020 Elliptic quantum groups.Verte

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书目名称Elliptic Quantum Groups
副标题Representations and
编辑Hitoshi Konno
视频video
概述Provides the first survey of elliptic quantum groups.Describes the elliptic quantum group concretely and pedagogically in the simplest setting.Contains finite and infinite dimensional representations
丛书名称SpringerBriefs in Mathematical Physics
图书封面Titlebook: Elliptic Quantum Groups; Representations and Hitoshi Konno Book 2020 Springer Nature Singapore Pte Ltd. 2020 Elliptic quantum groups.Verte
描述This is the first book on elliptic quantum groups, i.e., quantum groups associated to elliptic solutions of the Yang-Baxter equation. Based on research by the author and his collaborators, the book presents a comprehensive survey on the subject including a brief history of formulations and applications, a detailed formulation of the elliptic quantum group in the Drinfeld realization,  explicit  construction of both finite and infinite-dimensional representations, and  a construction of the vertex operators as intertwining operators of these representations. The vertex operators are important objects in representation theory of quantum groups.  In this book, they are used to derive the elliptic q-KZ equations and their elliptic hypergeometric integral solutions. In particular, the so-called elliptic weight functions appear in such solutions.  The author’s recent study showed that these elliptic weight functions are identified with Okounkov’s elliptic stableenvelopes for certain equivariant elliptic cohomology and play an important role to construct geometric representations of elliptic quantum groups. Okounkov’s  geometric approach to quantum integrable systems is a rapidly growing
出版日期Book 2020
关键词Elliptic quantum groups; Vertex operators; q-KZ equations; Elliptic stable envelopes; Quantum integrable
版次1
doihttps://doi.org/10.1007/978-981-15-7387-3
isbn_softcover978-981-15-7386-6
isbn_ebook978-981-15-7387-3Series ISSN 2197-1757 Series E-ISSN 2197-1765
issn_series 2197-1757
copyrightSpringer Nature Singapore Pte Ltd. 2020
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Projections and Projection Matrices, (quantum) equivariant cohomology, and deformed .-algebras. A brief history of elliptic quantum groups is also given. There are some different formulations developed independently and sometimes dependently. They are classified by their generators and co-algebra structures into the following three :
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Eugenius Kaszkurewicz,Amit Bhayaquantum group modules. In this chapter, we discuss the vertex operators of the .-modules. There are two types of them, type I and II, due to an asymmetry of the comultiplication with respect to the tensor components. By using the evaluation representation and the level-1 highest weight representatio
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Multi-field Coupling Numerical Simulation, Varchenko, Astérisque . (1997); Mimachi, Duke Math. J. ., 635–658 (1996); Matsuo, Comm. Math. Phys. ., 263–273 (1993)). Recently it has been shown (Gorbounov et al., J. Geom. Phys. ., 56–86 (2013); Rimányi et al., J. Geom. Phys. ., 81–119 (2015)) that they can be identified with the stable envelope
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Marc Arnaudon,Frédéric Barbaresco,Le Yang elliptic .-KZ equation. A key to this is a cyclic property of trace and the exchange relation of the vertex operators. Evaluating the trace explicitly we also give an elliptic hypergeometric integral solution to the equation (Konno, J. Integrable Syst. ., 1–43 (2017)).
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