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

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Eugenius Kaszkurewicz,Amit Bhayan constructed in the last chapter, we solve the intertwining relations and obtain a realization of the vertex operators explicitly. Exchange relations among the vertex operators are also given. Thus obtained vertex operators become a key to the rest of this book.

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An Introduction to Vector Spaces,n be identified with .. Based on this identification, we also show a correspondence between the Gelfand-Tsetlin basis (resp. the standard basis) of . in Chap. . and the fixed point classes (resp. the stable classes) in E.(.). This correspondence allows us to construct an action of . on E.(.).

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Introduction, (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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Elliptic Quantum Group ,, of the loop generators of the affine Lie algebra .. We call their generating functions the elliptic currents. The dynamical nature of . is realized by introducing the dynamical parameter . and considering a copy . of the Cartan subalgebra .. We take the field . of meromorphic functions on .. as the

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The ,-Hopf-Algebroid Structure of ,,E. Koelink, H. Rosengren, Acta. Appl. Math. ., 163–220 (2001); Konno, J. Geom. Phys. ., 1485–1511 (2009); Y. van Norden, Dynamical Quantum Groups, Duality and Special Functions, Ph.D. Thesis, 2005). A key idea is introducing an extended tensor product ., on which the dynamical coefficients from . ge

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Representations of ,,infinite dimensional representations of .. As examples, we present the evaluation representation associated with the vector representation (Sect. 4.2) and the level-1 highest weight representations (Sect. 4.3). Most of them can be extended to . for arbitrary untwisted affine Lie algebra . (Jimbo et

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