Combinatorics of Coxeter Groups / Anders Bjorner (2005)  

Público ISBD Título : Combinatorics of Coxeter Groups Tipo de documento: documento electrónico Autores: Anders Bjorner ; SpringerLink (Online service) ; Francesco Brenti Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2005 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 231 Número de páginas: XIV, 366 p Il.: online resource ISBN/ISSN/DL: 978-3-540-27596-1 Idioma : Inglés (eng) Palabras clave: Mathematics  Group  theory  Topological  groups  Lie  Combinatorics  Groups,  Groups  Theory  and  Generalizations Clasificación: 51 Matemáticas Resumen: Coxeter groups are of central importance in several areas of algebra, geometry, and combinatorics. This clear and rigorous exposition focuses on the combinatorial aspects of Coxeter groups, such as reduced expressions, partial order of group elements, enumeration, associated graphs and combinatorial cell complexes, and connections with combinatorial representation theory. While Coxeter groups have already been exposited from algebraic and geometric perspectives, this text is the first one to focus mainly on the combinatorial aspects of Coxeter groups. The first part of the book provides a self-contained introduction to combinatorial Coxeter group theory. The emphasis here is on the combinatorics of reduced decompositions, Bruhat order, weak order, and some aspects of root systems. The second part deals with more advanced topics, such as Kazhdan-Lusztig polynomials and representations, enumeration, and combinatorial descriptions of the classical finite and affine Weyl groups. A wide variety of exercises, ranging from easy to quite difficult are also included. The book will serve graduate students as well as researchers. Anders Björner is Professor of Mathematics at the Royal Institute of Technology in Stockholm, Sweden. Francesco Brenti is Professor of Mathematics at the University of Rome Nota de contenido: I -- The basics -- Bruhat order -- Weak order and reduced words -- Roots, games, and automata -- II -- Kazhdan-Lusztig and R-polynomials -- Kazhdan-Lusztig representations -- Enumeration -- Combinatorial Descriptions En línea: http://dx.doi.org/10.1007/3-540-27596-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35283 Combinatorics of Coxeter Groups [documento electrónico] / Anders Bjorner ; SpringerLink (Online service) ; Francesco Brenti . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2005 . - XIV, 366 p : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 231) . ISBN : 978-3-540-27596-1 Idioma : Inglés (eng) Palabras clave: Mathematics  Group  theory  Topological  groups  Lie  Combinatorics  Groups,  Groups  Theory  and  Generalizations Clasificación: 51 Matemáticas Resumen: Coxeter groups are of central importance in several areas of algebra, geometry, and combinatorics. This clear and rigorous exposition focuses on the combinatorial aspects of Coxeter groups, such as reduced expressions, partial order of group elements, enumeration, associated graphs and combinatorial cell complexes, and connections with combinatorial representation theory. While Coxeter groups have already been exposited from algebraic and geometric perspectives, this text is the first one to focus mainly on the combinatorial aspects of Coxeter groups. The first part of the book provides a self-contained introduction to combinatorial Coxeter group theory. The emphasis here is on the combinatorics of reduced decompositions, Bruhat order, weak order, and some aspects of root systems. The second part deals with more advanced topics, such as Kazhdan-Lusztig polynomials and representations, enumeration, and combinatorial descriptions of the classical finite and affine Weyl groups. A wide variety of exercises, ranging from easy to quite difficult are also included. The book will serve graduate students as well as researchers. Anders Björner is Professor of Mathematics at the Royal Institute of Technology in Stockholm, Sweden. Francesco Brenti is Professor of Mathematics at the University of Rome Nota de contenido: I -- The basics -- Bruhat order -- Weak order and reduced words -- Roots, games, and automata -- II -- Kazhdan-Lusztig and R-polynomials -- Kazhdan-Lusztig representations -- Enumeration -- Combinatorial Descriptions En línea: http://dx.doi.org/10.1007/3-540-27596-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35283

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Configuration Spaces / SpringerLink (Online service) ; Anders Bjorner ; Frederick Cohen ; C. de Concini ; Claudio Procesi ; Salvetti, M (2012)  

Público ISBD Título : Configuration Spaces : Geometry, Combinatorics and Topology Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Anders Bjorner ; Frederick Cohen ; C. de Concini ; Claudio Procesi ; Salvetti, M Editorial: Pisa : Scuola Normale Superiore Fecha de publicación: 2012 Colección: CRM Series Número de páginas: XXII, 536 p Il.: online resource ISBN/ISSN/DL: 978-88-7642-431-1 Idioma : Inglés (eng) Palabras clave: Mathematics  Geometry  Algebraic  topology  Combinatorics  Topology Clasificación: 51 Matemáticas Resumen: These proceedings contain the contributions of some of the participants in the "intensive research period" held at the De Giorgi Research Center in Pisa, during the period May–June 2010. The central theme of this research period was the study of configuration spaces from various points of view. This topic originated from the intersection of several classical theories: Braid groups and related topics, configurations of vectors (of great importance in Lie theory and representation theory), arrangements of hyperplanes and of subspaces, combinatorics, singularity theory. Recently, however, configuration spaces have acquired independent interest and indeed the contributions in this volume go far beyond the above subjects, making it attractive to a large audience of mathematicians Nota de contenido: On the structure of spaces of commuting elements in compact Lie groups -- On the fundamental group of the complement of two real tangent conics and an arbitrary number of real tangent lines -- Intersection cohomology of a rank one local system on the complement of a hyperplane-like divisor -- Characters of fundamental groups of curve complements and orbifold pencils -- A survey of some recent results concerning polyhedral products -- Analytic continuation of a parametric polytope and wall-crossing -- Embeddings of braid groups into mapping class groups and their homology -- The cohomology of the braid group B3 and of SL2(Z) with coefficients in a geometric representation -- Pure braid groups are not residually free -- Hodge–Deligne equivariant polynomials and monodromy of hyperplane arrangements -- The contravariant form on singular vectors of a projective arrangement -- Fox–Neuwirth cell structures and the cohomology of symmetric groups -- Basic questions on Artin–Tits groups -- Rational cohomology of the real Coxeter toric variety of type A -- Arrangements stable under the Coxeter groups -- Quantum and homological representations of braid groups -- Cohomology of the complement to an elliptic arrangement -- Residual nilpotence for generalizations of pure braid groups -- Some topological problems on the configuration spaces of Artin and Coxeter groups -- Chromatic quasisymmetric functions and Hessenberg varieties -- Geometric and homological finiteness in free abelian covers -- Minimal stratifications for line arrangements and positive homogeneous presentations for fundamental groups En línea: http://dx.doi.org/10.1007/978-88-7642-431-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33054 Configuration Spaces : Geometry, Combinatorics and Topology [documento electrónico] / SpringerLink (Online service) ; Anders Bjorner ; Frederick Cohen ; C. de Concini ; Claudio Procesi ; Salvetti, M . - Pisa : Scuola Normale Superiore, 2012 . - XXII, 536 p : online resource. - (CRM Series) . ISBN : 978-88-7642-431-1 Idioma : Inglés (eng) Palabras clave: Mathematics  Geometry  Algebraic  topology  Combinatorics  Topology Clasificación: 51 Matemáticas Resumen: These proceedings contain the contributions of some of the participants in the "intensive research period" held at the De Giorgi Research Center in Pisa, during the period May–June 2010. The central theme of this research period was the study of configuration spaces from various points of view. This topic originated from the intersection of several classical theories: Braid groups and related topics, configurations of vectors (of great importance in Lie theory and representation theory), arrangements of hyperplanes and of subspaces, combinatorics, singularity theory. Recently, however, configuration spaces have acquired independent interest and indeed the contributions in this volume go far beyond the above subjects, making it attractive to a large audience of mathematicians Nota de contenido: On the structure of spaces of commuting elements in compact Lie groups -- On the fundamental group of the complement of two real tangent conics and an arbitrary number of real tangent lines -- Intersection cohomology of a rank one local system on the complement of a hyperplane-like divisor -- Characters of fundamental groups of curve complements and orbifold pencils -- A survey of some recent results concerning polyhedral products -- Analytic continuation of a parametric polytope and wall-crossing -- Embeddings of braid groups into mapping class groups and their homology -- The cohomology of the braid group B3 and of SL2(Z) with coefficients in a geometric representation -- Pure braid groups are not residually free -- Hodge–Deligne equivariant polynomials and monodromy of hyperplane arrangements -- The contravariant form on singular vectors of a projective arrangement -- Fox–Neuwirth cell structures and the cohomology of symmetric groups -- Basic questions on Artin–Tits groups -- Rational cohomology of the real Coxeter toric variety of type A -- Arrangements stable under the Coxeter groups -- Quantum and homological representations of braid groups -- Cohomology of the complement to an elliptic arrangement -- Residual nilpotence for generalizations of pure braid groups -- Some topological problems on the configuration spaces of Artin and Coxeter groups -- Chromatic quasisymmetric functions and Hessenberg varieties -- Geometric and homological finiteness in free abelian covers -- Minimal stratifications for line arrangements and positive homogeneous presentations for fundamental groups En línea: http://dx.doi.org/10.1007/978-88-7642-431-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33054

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