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Titlebook: Affine Flag Manifolds and Principal Bundles; Alexander Schmitt Conference proceedings 2010 Birkhäuser Basel 2010 Dimension.algebraic geome

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发表于 2025-3-21 19:26:50 | 显示全部楼层 |阅读模式
期刊全称Affine Flag Manifolds and Principal Bundles
影响因子2023Alexander Schmitt
视频video
发行地址User-friendly introductions to interesting fields of active current research.Contributions written by internationally renowned experts.No textbooks available on these topics so far.Includes supplement
学科分类Trends in Mathematics
图书封面Titlebook: Affine Flag Manifolds and Principal Bundles;  Alexander Schmitt Conference proceedings 2010 Birkhäuser Basel 2010 Dimension.algebraic geome
影响因子Affine flag manifolds are infinite dimensional versions of familiar objects such as Graßmann varieties. The book features lecture notes, survey articles, and research notes - based on workshops held in Berlin, Essen, and Madrid - explaining the significance of these and related objects (such as double affine Hecke algebras and affine Springer fibers) in representation theory (e.g., the theory of symmetric polynomials), arithmetic geometry (e.g., the fundamental lemma in the Langlands program), and algebraic geometry (e.g., affine flag manifolds as parameter spaces for principal bundles). Novel aspects of the theory of principal bundles on algebraic varieties are also studied in the book.
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发表于 2025-3-22 00:09:26 | 显示全部楼层
Lectures on the Moduli Stack of Vector Bundles on a Curve,o introduce the notion of algebraic stacks and to illustrate how one can work with these objects. Applications given are the (non-)existence of universal families on coarse moduli spaces and the computation of the cohomology of the moduli stack.
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Clifford Indices for Vector Bundles on Curves,tions of a line bundle. This is the first step in distinguishing curves of the same genus. In this paper we generalise this to introduce Clifford indices for semistable vector bundles on curves. We study these invariants, giving some basic properties and carrying out some computations for small rank
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Division Algebras and Unit Groups on Surfaces, theory of vector bundles over curves resp. surfaces. Two different kinds of modifications of bundles and concepts of connectivity between such bundles are introduced. There are various computations of Chern classes of the bundles involved.
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Double Affine Hecke Algebras and Affine Flag Manifolds, I,in the main results of the authors on its representation theory. There are also some simplifications of the original arguments and proofs for some well-known results for which there exists no reference.
发表于 2025-3-22 17:43:08 | 显示全部楼层
A Physics Perspective on Geometric Langlands Duality,like covariance in differential geometry). Furthermore, it leads to an approach toward geometric Langlands duality for algebraic surfaces, reproducing and extending the recent results of Braverman and Finkelberg.
发表于 2025-3-22 22:51:42 | 显示全部楼层
Conference proceedings 2010the fundamental lemma in the Langlands program), and algebraic geometry (e.g., affine flag manifolds as parameter spaces for principal bundles). Novel aspects of the theory of principal bundles on algebraic varieties are also studied in the book.
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