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Titlebook: Shuffle Approach Towards Quantum Affine and Toroidal Algebras; Alexander Tsymbaliuk Book 2023 The Author(s), under exclusive license to Sp

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发表于 2025-3-21 17:36:19 | 显示全部楼层 |阅读模式
书目名称Shuffle Approach Towards Quantum Affine and Toroidal Algebras
编辑Alexander Tsymbaliuk
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概述Shuffle approach is a powerful technique in treating both algebraic and geometric aspects of quantum affinized algebras.Collects in one volume information about shuffle algebras which usually is sprea
丛书名称SpringerBriefs in Mathematical Physics
图书封面Titlebook: Shuffle Approach Towards Quantum Affine and Toroidal Algebras; Alexander Tsymbaliuk Book 2023 The Author(s), under exclusive license to Sp
描述This book is based on the author‘s mini course delivered at Tokyo University of Marine Science and Technology in March 2019. .The shuffle approach to Drinfeld–Jimbo quantum groups of finite type (embedding their "positive" subalgebras into q-deformed shuffle algebras) was first developed independently in the 1990s by J. Green, M. Rosso, and P. Schauenburg. Motivated by similar ideas, B. Feigin and A. Odesskii proposed a shuffle approach to elliptic quantum groups around the same time. The shuffle algebras in the present book can be viewed as trigonometric degenerations of the Feigin–Odesskii elliptic shuffle algebras. They provide combinatorial models for the "positive" subalgebras of quantum affine algebras in their loop realizations. These algebras appeared first in that context in the work of B. Enriquez..Over the last decade, the shuffle approach has been applied to various problems in combinatorics (combinatorics of Macdonald polynomials and Dyck paths, generalization to wreath Macdonald polynomials and operators), geometric representation theory (especially the study of quantum algebras’ actions on the equivariant K-theories of various moduli spaces such as affine Laumon spac
出版日期Book 2023
关键词Shuffle Approach; Quantum Affine Algebras; Quantum Toroidal Algebras; Representation Theory; Combinatori
版次1
doihttps://doi.org/10.1007/978-981-99-3150-7
isbn_softcover978-981-99-3149-1
isbn_ebook978-981-99-3150-7Series ISSN 2197-1757 Series E-ISSN 2197-1765
issn_series 2197-1757
copyrightThe Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023
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发表于 2025-3-21 23:52:24 | 显示全部楼层
Quantum Loop ,, Its Two Integral Forms, and Generalizations,nstruct a family of PBWD (Poincaré-Birkhoff-Witt-Drinfeld) bases for the quantum loop algebra . in the new Drinfeld realization. The shuffle approach also allows to strengthen this by constructing a family of PBWD bases for the RTT form (arising naturally from a different, historically the first, re
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发表于 2025-3-22 02:13:04 | 显示全部楼层
Quantum Toroidal ,, Its Representations, and Geometric Realization,elliptic Hall algebra of [.], which provides its “90 degree rotation” automorphism . (first discovered in [.]). We also establish the shuffle realization of its “positive” subalgebra and its particular commutative subalgebra, due to [., .], respectively. Following [., ., .], we discuss a combinatori
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发表于 2025-3-22 05:56:36 | 显示全部楼层
Quantum Toroidal ,, Its Representations, and Geometric Realization,e some flavor of the applications to the geometry by realizing Fock modules and their tensor products via equivariant .-theory of the Gieseker moduli spaces, as well as evoking the .-theoretic version of the Nakajima’s construction from [.].
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发表于 2025-3-22 12:08:37 | 显示全部楼层
Book 2023Drinfeld–Jimbo quantum groups of finite type (embedding their "positive" subalgebras into q-deformed shuffle algebras) was first developed independently in the 1990s by J. Green, M. Rosso, and P. Schauenburg. Motivated by similar ideas, B. Feigin and A. Odesskii proposed a shuffle approach to ellipt
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Alexander TsymbaliukShuffle approach is a powerful technique in treating both algebraic and geometric aspects of quantum affinized algebras.Collects in one volume information about shuffle algebras which usually is sprea
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SpringerBriefs in Mathematical Physicshttp://image.papertrans.cn/s/image/866792.jpg
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发表于 2025-3-23 05:46:55 | 显示全部楼层
978-981-99-3149-1The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023
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