Oliver Lorscheid's Books

Quiver Grassmannians of Extended Dynkin Type D Part I: Schubert Systems and Decompositions into Affine Spaces

By: Oliver Lorscheid,Thorsten Weist

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Quiver Grassmannians of Extended Dynkin Type D Part I: Schubert Systems and Decompositions into Affine Spaces

By: Oliver Lorscheid,Thorsten Weist

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.

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American Mathematical Soc.

Published Date

ISBN 10

1470436477

ISBN 13

9781470436476

Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type

By: Carles Broto,Jesper M. Møller,Bob Oliver

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Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type

By: Carles Broto,Jesper M. Møller,Bob Oliver

For a finite group G of Lie type and a prime p, the authors compare the automorphism groups of the fusion and linking systems of G at p with the automorphism group of G itself. When p is the defining characteristic of G, they are all isomorphic, with a very short list of exceptions. When p is different from the defining characteristic, the situation is much more complex but can always be reduced to a case where the natural map from Out(G) to outer automorphisms of the fusion or linking system is split surjective. This work is motivated in part by questions involving extending the local structure of a group by a group of automorphisms, and in part by wanting to describe self homotopy equivalences of BG∧p in terms of Out(G).

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176

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470437724

ISBN 13

9781470437725

Quiver Grassmannians of Extended Dynkin Type D Part I: Schubert Systems and Decompositions into Affine Spaces

By: Oliver Lorscheid,Thorsten Weist

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Quiver Grassmannians of Extended Dynkin Type D Part I: Schubert Systems and Decompositions into Affine Spaces

By: Oliver Lorscheid,Thorsten Weist

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Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470436477

ISBN 13

9781470436476

Quiver Grassmannians of Extended Dynkin Type D.

Schubert systems and decompositions into affine spaces

By: Oliver Lorscheid,Thorsten Weist

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Quiver Grassmannians of Extended Dynkin Type D.

Schubert systems and decompositions into affine spaces

By: Oliver Lorscheid,Thorsten Weist

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.

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ISBN 10

1470453991

ISBN 13

9781470453992

Book's by Oliver Lorscheid

Quiver Grassmannians of Extended Dynkin Type D Part I: Schubert Systems and Decompositions into Affine Spaces

Quiver Grassmannians of Extended Dynkin Type D Part I: Schubert Systems and Decompositions into Affine Spaces

Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type

Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type

Quiver Grassmannians of Extended Dynkin Type D Part I: Schubert Systems and Decompositions into Affine Spaces

Quiver Grassmannians of Extended Dynkin Type D Part I: Schubert Systems and Decompositions into Affine Spaces

Quiver Grassmannians of Extended Dynkin Type D.

Quiver Grassmannians of Extended Dynkin Type D.

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