Quiver Grassmannians Of Extended Dynkin Type D Part I Schubert Systems And Decompositions Into Affine Spaces
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Quiver Grassmannians Of Extended Dynkin Type D Part I Schubert Systems And Decompositions Into Affine Spaces
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Author : Oliver Lorscheid
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-12-02
Quiver Grassmannians Of Extended Dynkin Type D Part I Schubert Systems And Decompositions Into Affine Spaces written by Oliver Lorscheid and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-02 with Education categories.
Let Q be a quiver of extended Dynkin type D˜n. In this first of two papers, the authors show that the quiver Grassmannian Gre–(M) has a decomposition into affine spaces for every dimension vector e– and every indecomposable representation M of defect −1 and defect 0, with the exception of the non-Schurian representations in homogeneous tubes. The authors characterize the affine spaces in terms of the combinatorics of a fixed coefficient quiver for M. The method of proof is to exhibit explicit equations for the Schubert cells of Gre–(M) and to solve this system of equations successively in linear terms. This leads to an intricate combinatorial problem, for whose solution the authors develop the theory of Schubert systems. In Part 2 of this pair of papers, they extend the result of this paper to all indecomposable representations M of Q and determine explicit formulae for the F-polynomial of M.
Quiver Grassmannians Of Extended Dynkin Type D
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Author : Oliver Lorscheid
language : en
Publisher:
Release Date : 2019
Quiver Grassmannians Of Extended Dynkin Type D written by Oliver Lorscheid and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Electronic books categories.
Let Q be a quiver of extended Dynkin type \widetildeD}_n. In this first of two papers, the authors show that the quiver Grassmannian \mathrmGr}_{underline{e}}(M) has a decomposition into affine spaces for every dimension vector underlinee} and every indecomposable representation M of defect -1 and defect 0, with the exception of the non-Schurian representations in homogeneous tubes. The authors characterize the affine spaces in terms of the combinatorics of a fixed coefficient quiver for M. The method of proof is to exhibit explicit equations for the Schubert cells of \mathrmGr}_{underline{e}}(M) and to solve this system of equations successively in linear terms. This leads to an intricate combinatorial problem, for whose solution the authors develop the theory of Schubert systems. In Part 2 of this pair of papers, they extend the result of this paper to all indecomposable representations M of Q and determine explicit formulae for the F-polynomial of M.
Quiver Grassmannians Of Extended Dynkin Type D
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Author : Oliver Lorscheid
language : en
Publisher:
Release Date : 2019
Quiver Grassmannians Of Extended Dynkin Type D written by Oliver Lorscheid and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
Representation Theory And Beyond
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Author : Jan Šťovíček
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-11-13
Representation Theory And Beyond written by Jan Šťovíček and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-13 with Education categories.
This volume contains the proceedings of the Workshop and 18th International Conference on Representations of Algebras (ICRA 2018) held from August 8–17, 2018, in Prague, Czech Republic. It presents several themes of contemporary representation theory together with some new tools, such as stable ∞ ∞-categories, stable derivators, and contramodules. In the first part, expanded lecture notes of four courses delivered at the workshop are presented, covering the representation theory of finite sets with correspondences, geometric theory of quiver Grassmannians, recent applications of contramodules to tilting theory, as well as symmetries in the representation theory over an abstract stable homotopy theory. The second part consists of six more-advanced papers based on plenary talks of the conference, presenting selected topics from contemporary representation theory: recollements and purity, maximal green sequences, cohomological Hall algebras, Hochschild cohomology of associative algebras, cohomology of local selfinjective algebras, and the higher Auslander–Reiten theory studied via homotopy theory.
Subgroup Decomposition In Out Fn
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Author : Michael Handel
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-05-13
Subgroup Decomposition In Out Fn written by Michael Handel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-13 with Education categories.
In this work the authors develop a decomposition theory for subgroups of Out(Fn) which generalizes the decomposition theory for individual elements of Out(Fn) found in the work of Bestvina, Feighn, and Handel, and which is analogous to the decomposition theory for subgroups of mapping class groups found in the work of Ivanov.
Conformal Graph Directed Markov Systems On Carnot Groups
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Author : Vasileios Chousionis
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28
Conformal Graph Directed Markov Systems On Carnot Groups written by Vasileios Chousionis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.
The authors develop a comprehensive theory of conformal graph directed Markov systems in the non-Riemannian setting of Carnot groups equipped with a sub-Riemannian metric. In particular, they develop the thermodynamic formalism and show that, under natural hypotheses, the limit set of an Carnot conformal GDMS has Hausdorff dimension given by Bowen's parameter. They illustrate their results for a variety of examples of both linear and nonlinear iterated function systems and graph directed Markov systems in such sub-Riemannian spaces. These include the Heisenberg continued fractions introduced by Lukyanenko and Vandehey as well as Kleinian and Schottky groups associated to the non-real classical rank one hyperbolic spaces.
Affine Flag Varieties And Quantum Symmetric Pairs
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Author : Zhaobing Fan
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28
Affine Flag Varieties And Quantum Symmetric Pairs written by Zhaobing Fan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.
The quantum groups of finite and affine type $A$ admit geometric realizations in terms of partial flag varieties of finite and affine type $A$. Recently, the quantum group associated to partial flag varieties of finite type $B/C$ is shown to be a coideal subalgebra of the quantum group of finite type $A$.
Nonlinear Diffusion Equations And Curvature Conditions In Metric Measure Spaces
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Author : Luigi Ambrosio
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-02-13
Nonlinear Diffusion Equations And Curvature Conditions In Metric Measure Spaces written by Luigi Ambrosio and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-13 with Education categories.
The aim of this paper is to provide new characterizations of the curvature dimension condition in the context of metric measure spaces (X,d,m). On the geometric side, the authors' new approach takes into account suitable weighted action functionals which provide the natural modulus of K-convexity when one investigates the convexity properties of N-dimensional entropies. On the side of diffusion semigroups and evolution variational inequalities, the authors' new approach uses the nonlinear diffusion semigroup induced by the N-dimensional entropy, in place of the heat flow. Under suitable assumptions (most notably the quadraticity of Cheeger's energy relative to the metric measure structure) both approaches are shown to be equivalent to the strong CD∗(K,N) condition of Bacher-Sturm.
New Complex Analytic Methods In The Study Of Non Orientable Minimal Surfaces In Rn
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Author : Antonio Alarcón
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-05-13
New Complex Analytic Methods In The Study Of Non Orientable Minimal Surfaces In Rn written by Antonio Alarcón and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-13 with Education categories.
All the new tools mentioned above apply to non-orientable minimal surfaces endowed with a fixed choice of a conformal structure. This enables the authors to obtain significant new applications to the global theory of non-orientable minimal surfaces. In particular, they construct proper non-orientable conformal minimal surfaces in Rn with any given conformal structure, complete non-orientable minimal surfaces in Rn with arbitrary conformal type whose generalized Gauss map is nondegenerate and omits n hyperplanes of CPn−1 in general position, complete non-orientable minimal surfaces bounded by Jordan curves, and complete proper non-orientable minimal surfaces normalized by bordered surfaces in p-convex domains of Rn.
Geometric Optics For Surface Waves In Nonlinear Elasticity
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Author : Jean-François Coulombel
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-04-03
Geometric Optics For Surface Waves In Nonlinear Elasticity written by Jean-François Coulombel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-03 with Education categories.
This work is devoted to the analysis of high frequency solutions to the equations of nonlinear elasticity in a half-space. The authors consider surface waves (or more precisely, Rayleigh waves) arising in the general class of isotropic hyperelastic models, which includes in particular the Saint Venant-Kirchhoff system. Work has been done by a number of authors since the 1980s on the formulation and well-posedness of a nonlinear evolution equation whose (exact) solution gives the leading term of an approximate Rayleigh wave solution to the underlying elasticity equations. This evolution equation, which is referred to as “the amplitude equation”, is an integrodifferential equation of nonlocal Burgers type. The authors begin by reviewing and providing some extensions of the theory of the amplitude equation. The remainder of the paper is devoted to a rigorous proof in 2D that exact, highly oscillatory, Rayleigh wave solutions uε to the nonlinear elasticity equations exist on a fixed time interval independent of the wavelength ε, and that the approximate Rayleigh wave solution provided by the analysis of the amplitude equation is indeed close in a precise sense to uε on a time interval independent of ε. This paper focuses mainly on the case of Rayleigh waves that are pulses, which have profiles with continuous Fourier spectrum, but the authors' method applies equally well to the case of wavetrains, whose Fourier spectrum is discrete.