Rouquier, Raphaël
Overview
Works:  14 works in 34 publications in 3 languages and 313 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Editor, Thesis advisor, Author 
Publication Timeline
.
Most widely held works by
Raphaël Rouquier
Triangulated categories(
Book
)
16 editions published in 2010 in English and Undetermined and held by 276 WorldCat member libraries worldwide
"This volume grew out of a Workshop on Triangulated Categories held at the University of Leeds in August 2006. The meeting, a Satellite of the International Congress of Mathematicians 2006, has been generously supported by the Leverhulme Foundation (via the network Algebras, Representations and Applications), the London Mathematical Society (Conference Grant Ref. 1438) and the University of Leeds. Over the past decades, triangulated categories have made their way into many different parts of mathematics, to the extent that today, they can be viewed as a unifying theory underlying major parts of modern mathematics. The Leeds workshop has brought together researchers from many parts of mathematics who all use triangulated methods but would not usually meet at more specialized conferences, with the aim to promote cross fertilization leading to new applications of triangulated categories. The present book collects surveys by leading experts reflecting a broad range of important topics covered at the workshop. However, it is not a proceedings volume recording precisely the talks given at the conference and it does not claim to be a comprehensive coverage of all the numerous applications of triangulated categories throughout mathematics"Résumé de l'éditeur
16 editions published in 2010 in English and Undetermined and held by 276 WorldCat member libraries worldwide
"This volume grew out of a Workshop on Triangulated Categories held at the University of Leeds in August 2006. The meeting, a Satellite of the International Congress of Mathematicians 2006, has been generously supported by the Leverhulme Foundation (via the network Algebras, Representations and Applications), the London Mathematical Society (Conference Grant Ref. 1438) and the University of Leeds. Over the past decades, triangulated categories have made their way into many different parts of mathematics, to the extent that today, they can be viewed as a unifying theory underlying major parts of modern mathematics. The Leeds workshop has brought together researchers from many parts of mathematics who all use triangulated methods but would not usually meet at more specialized conferences, with the aim to promote cross fertilization leading to new applications of triangulated categories. The present book collects surveys by leading experts reflecting a broad range of important topics covered at the workshop. However, it is not a proceedings volume recording precisely the talks given at the conference and it does not claim to be a comprehensive coverage of all the numerous applications of triangulated categories throughout mathematics"Résumé de l'éditeur
On complex reflection groups and their associated braid groups by
Michel Broué(
Book
)
3 editions published in 1994 in English and German and held by 6 WorldCat member libraries worldwide
3 editions published in 1994 in English and German and held by 6 WorldCat member libraries worldwide
Catégories dérivées et variétés de DeligneLusztig. Moduli spaces of Abelian differentials : the principal boundary,
counting problems, and the SiegelVeech constants / by Alex Eskin, Howard Masur, and Anton Zorich [u.a.] by
Cédric Bonnafé(
Book
)
1 edition published in 2003 in English and held by 5 WorldCat member libraries worldwide
1 edition published in 2003 in English and held by 5 WorldCat member libraries worldwide
Familles de caractères de groupes de réflexions complexes by
Gunter Malle(
Book
)
1 edition published in 2003 in French and held by 5 WorldCat member libraries worldwide
1 edition published in 2003 in French and held by 5 WorldCat member libraries worldwide
Catégories dérivées et variétés de DeligneLusztig(
Book
)
2 editions published in 2003 in Undetermined and French and held by 4 WorldCat member libraries worldwide
2 editions published in 2003 in Undetermined and French and held by 4 WorldCat member libraries worldwide
ISOMETRIES PARFAITES DANS LES GROUPES FINIS by
Raphaël Rouquier(
Book
)
2 editions published in 1992 in French and held by 3 WorldCat member libraries worldwide
SUIVANT M. BROUE, NOUS ETUDIONS CERTAINES ISOMETRIES ENTRE GROUPES DE GROTHENDIECK DE BLOCS A DEFAUT ABELIEN DE GROUPES SYMETRIQUES ET SPORADIQUES, QUI COMMUTENT AVEC LES APPLICATIONS DE DECOMPOSITION GENERALISEES
2 editions published in 1992 in French and held by 3 WorldCat member libraries worldwide
SUIVANT M. BROUE, NOUS ETUDIONS CERTAINES ISOMETRIES ENTRE GROUPES DE GROTHENDIECK DE BLOCS A DEFAUT ABELIEN DE GROUPES SYMETRIQUES ET SPORADIQUES, QUI COMMUTENT AVEC LES APPLICATIONS DE DECOMPOSITION GENERALISEES
Catégories dérivées et variétés de DeligneLusztig / the principal boundary counting problems, and the SiegelVeech constants
/ by Alex Eskin, Howard Masur and Anton Zorich. Convexes hyperboliques et fonctions quasisymétriques / par Yves Benoist.
The ConnesKasparov conjecture for almost connected groups and for linear padic groups / by Jérôme Chabert, Siegfried Echterhoff
and Ryszard Nest by
Cédric Bonnafé(
Book
)
1 edition published in 2003 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 2003 in English and held by 3 WorldCat member libraries worldwide
Autour de la catégorie des bimodules de Soergel by
Nicolas Libedinsky(
Book
)
1 edition published in 2008 in French and held by 2 WorldCat member libraries worldwide
My thesis is about Soergel category of bimodules. This tensorial category, associated to any Coxeter group can be seen as a categorification of the corresponding Hecke algebra. This category represents the main way of combinatorial and algebraic attack of the problems of formulae of characters in positive characteristic. It is also linked to the questions of positivity of KazhdanLusztig polynomials (via "Soergel conjecture") and to some homological invariants of knots. In my thesis, I study Soergel category of bimodules from a combinatorial point of view. My first result is the construction of explicit bases for the morphisms spaces in Soergel category. This is a first step towards the description by generators and relations of Soergel categories. In a second work I obtain this description by generators and relations for rightangled Coxeter groups. In a third work I prove that we obtain the same indecomposable bimodules working with the geometrie representation of a Coxeter group or working with the reflection representations considered by Soergel. Finally in my last work I construct explicitly a set of idempotents in Soergel category for "large" Coxeter Systems (every product of simple reflections are at least of order four). Thus we obtain a new natural basis of the Hecke algebra between the KazhdanLusztig basis and the "BottSamelsonDemazure" basis that actually corresponds to Soergel bimodules
1 edition published in 2008 in French and held by 2 WorldCat member libraries worldwide
My thesis is about Soergel category of bimodules. This tensorial category, associated to any Coxeter group can be seen as a categorification of the corresponding Hecke algebra. This category represents the main way of combinatorial and algebraic attack of the problems of formulae of characters in positive characteristic. It is also linked to the questions of positivity of KazhdanLusztig polynomials (via "Soergel conjecture") and to some homological invariants of knots. In my thesis, I study Soergel category of bimodules from a combinatorial point of view. My first result is the construction of explicit bases for the morphisms spaces in Soergel category. This is a first step towards the description by generators and relations of Soergel categories. In a second work I obtain this description by generators and relations for rightangled Coxeter groups. In a third work I prove that we obtain the same indecomposable bimodules working with the geometrie representation of a Coxeter group or working with the reflection representations considered by Soergel. Finally in my last work I construct explicitly a set of idempotents in Soergel category for "large" Coxeter Systems (every product of simple reflections are at least of order four). Thus we obtain a new natural basis of the Hecke algebra between the KazhdanLusztig basis and the "BottSamelsonDemazure" basis that actually corresponds to Soergel bimodules
Correspondance de springer modulaire et matrices de décomposition by
Daniel Juteau(
Book
)
1 edition published in 2007 in English and held by 2 WorldCat member libraries worldwide
In 1976, Springer defined a correspondence making a link between the irreducible ordinary representations (in characteristic zero) of a Weyl group and the geometry of the associated nilpotent variety. In this thesis, we define a modular Springer correspondence (in positive characteristic), and we show that the decomposition numbers of a Weyl group (for example the symmetric group) are particular cases of decomposition numbers for equivalant perverse sheaves on the nilpotent variety. We determine this correspondence m the case of the symmetric group, and show that James's row and column removal rule is a consequence of a smooth equivalence of nilpotent singularises obtained by Kraft and Procesi. We also calculate explicitly the decomposition numbers associated to the regular and subregular classes, and to the minimal and trivial classes
1 edition published in 2007 in English and held by 2 WorldCat member libraries worldwide
In 1976, Springer defined a correspondence making a link between the irreducible ordinary representations (in characteristic zero) of a Weyl group and the geometry of the associated nilpotent variety. In this thesis, we define a modular Springer correspondence (in positive characteristic), and we show that the decomposition numbers of a Weyl group (for example the symmetric group) are particular cases of decomposition numbers for equivalant perverse sheaves on the nilpotent variety. We determine this correspondence m the case of the symmetric group, and show that James's row and column removal rule is a consequence of a smooth equivalence of nilpotent singularises obtained by Kraft and Procesi. We also calculate explicitly the decomposition numbers associated to the regular and subregular classes, and to the minimal and trivial classes
Correspondance de McKay et équivalences dérivées by
Magda Sebestean(
Book
)
1 edition published in 2005 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2005 in English and held by 2 WorldCat member libraries worldwide
Derived equivalences and finite dimensional algebras by
Raphaël Rouquier(
)
1 edition published in 2006 in English and held by 1 WorldCat member library worldwide
1 edition published in 2006 in English and held by 1 WorldCat member library worldwide
Le monstre gentil des mathematiciens by
Raphaël Rouquier(
)
1 edition published in 2001 in French and held by 1 WorldCat member library worldwide
1 edition published in 2001 in French and held by 1 WorldCat member library worldwide
Derived equivalences for group rings by
Steffen König(
Book
)
1 edition published in 1998 in English and held by 1 WorldCat member library worldwide
A selfcontained introduction is given to J. Rickard's Morita theory for derived module categories and its recent applications in representation theory of finite groups. In particular, Broué's conjecture is discussed, giving a structural explanation for relations between the pmodular character table of a finite group and that of its "plocal structure". The book is addressed to researchers or graduate students and can serve as material for a seminar. It surveys the current state of the field, and it also provides a "user's guide" to derived equivalences and tilting complexes. Results and proofs are presented in the generality needed for group theoretic applications
1 edition published in 1998 in English and held by 1 WorldCat member library worldwide
A selfcontained introduction is given to J. Rickard's Morita theory for derived module categories and its recent applications in representation theory of finite groups. In particular, Broué's conjecture is discussed, giving a structural explanation for relations between the pmodular character table of a finite group and that of its "plocal structure". The book is addressed to researchers or graduate students and can serve as material for a seminar. It surveys the current state of the field, and it also provides a "user's guide" to derived equivalences and tilting complexes. Results and proofs are presented in the generality needed for group theoretic applications
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Related Identities
 Jørgensen, Peter 1970 Artist Editor
 Holm, Thorsten 1965 Editor
 Bonnafé, Cédric Thesis advisor Author
 Malle, Gunter Author
 Broué, Michel 1946 Thesis advisor Author
 Zorich, Anton
 Eskin, Alex
 Université Paris Diderot  Paris 7 Degree grantor
 Masur, Howard
 Masur, Howard
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Alternative Names
Raphaël Rouquier Frans wiskundige
Raphaël Rouquier fransk matematikar
Raphaël Rouquier fransk matematiker
Raphaël Rouquier französischer Mathematiker
Raphaël Rouquier French mathematician
Raphaël Rouquier matemático francés
Raphaël Rouquier mathématicien français
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