Linear and Projective Representations of Symmetric Groups

Alexander Kleshchev

doi:10.1017/CBO9780511542800

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Linear and Projective Representations of Symmetric Groups

Linear and Projective Representations of Symmetric Groups

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Ariki, Susumu Mathas, Andrew and Rui, Hebing 2006. Cyclotomic Nazarov-Wenzl Algebras. Nagoya Mathematical Journal, Vol. 182, Issue. , p. 47.

CrossRef

Google Scholar

Khongsap, T A and Wang, Weiqiang 2008. Hecke-Clifford Algebras and Spin Hecke Algebras I: The Classical Affine Type. Transformation Groups, Vol. 13, Issue. 2, p. 389.

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Fotsing, Bosco 2008. On the Vertices of Simple Modules for Symmetric Groups. Communications in Algebra, Vol. 36, Issue. 11, p. 3980.

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Hill, David 2008. A Note on Weyl Modules for ∞and ∞. Communications in Algebra, Vol. 36, Issue. 12, p. 4375.

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Danz, Susanne 2008. Vertices of Low-Dimensional Simple Modules for Symmetric Groups. Communications in Algebra, Vol. 36, Issue. 12, p. 4521.

CrossRef

Google Scholar

Ruff, Oliver 2008. Weight Theory for Alternating Groups. Algebra Colloquium, Vol. 15, Issue. 03, p. 391.

CrossRef

Google Scholar

Wan, Jinkui and Wang, Weiqiang 2008. Modular Representations and Branching Rules for Wreath Hecke Algebras. International Mathematics Research Notices, Vol. 2008, Issue. ,

CrossRef

Google Scholar

Miemietz, Vanessa 2008. On Representations of Affine Hecke Algebras of Type B. Algebras and Representation Theory, Vol. 11, Issue. 4, p. 369.

CrossRef

Google Scholar

Arisha, Hussam and Schaps, Mary 2009. Maximal Strings in the Crystal Graph of Spin Representations of the Symmetric and Alternating Groups. Communications in Algebra, Vol. 37, Issue. 11, p. 3779.

CrossRef

Google Scholar

Brundan, Jonathan and Kleshchev, Alexander 2009. Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras. Inventiones mathematicae, Vol. 178, Issue. 3, p. 451.

CrossRef

Google Scholar

Tysse, Jill and Wang, Weiqiang 2009. The centers of spin symmetric group algebras and Catalan numbers. Journal of Algebraic Combinatorics, Vol. 29, Issue. 2, p. 175.

CrossRef

Google Scholar

Wan, Jinkui 2010. Completely splittable representations of affine Hecke-Clifford algebras. Journal of Algebraic Combinatorics, Vol. 32, Issue. 1, p. 15.

CrossRef

Google Scholar

Kleshchev, Alexander and Nash, David 2010. An Interpretation of the Lascoux–Leclerc–Thibon Algorithm and Graded Representation Theory. Communications in Algebra, Vol. 38, Issue. 12, p. 4489.

CrossRef

Google Scholar

Brundan, Jonathan and Kleshchev, Alexander 2010. The degenerate analogue of Ariki’s categorification theorem. Mathematische Zeitschrift, Vol. 266, Issue. 4, p. 877.

CrossRef

Google Scholar

Müller, Jürgen and Orlob, Johannes 2011. On the Structure of the Tensor Square of the Natural Module of the Symmetric Group. Algebra Colloquium, Vol. 18, Issue. 04, p. 589.

CrossRef

Google Scholar

Goodman, Frederick M. 2011. Admissibility Conditions for Degenerate Cyclotomic BMW Algebras. Communications in Algebra, Vol. 39, Issue. 2, p. 452.

CrossRef

Google Scholar

Hill, David Kujawa, Jonathan R. and Sussan, Joshua 2011. Degenerate affine Hecke–Clifford algebras and type Q Lie superalgebras. Mathematische Zeitschrift, Vol. 268, Issue. 3-4, p. 1091.

CrossRef

Google Scholar

Lee, Dong-il 2011. Basis theorem for degenerate affine Hecke algebras. p. 6260.

CrossRef

Google Scholar

Varagnolo, M. and Vasserot, E. 2011. Canonical bases and affine Hecke algebras of type B. Inventiones mathematicae, Vol. 185, Issue. 3, p. 593.

CrossRef

Google Scholar

Danz, Susanne and Erdmann, Karin 2012. The Vertices of a Class of Specht Modules and Simple Modules for Symmetric Groups in Characteristic 2. Algebra Colloquium, Vol. 19, Issue. spec01, p. 987.

CrossRef

Google Scholar

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Alexander Kleshchev, University of Oregon

Publisher: Cambridge University Press
Online publication date: January 2010
Print publication year: 2005
Online ISBN: 9780511542800
DOI: https://doi.org/10.1017/CBO9780511542800

Subjects: Recreational Mathematics, Mathematics, Algebra
Series: Cambridge Tracts in Mathematics (163)

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Linear and Projective Representations of Symmetric Groups
Alexander Kleshchev
Online ISBN: 9780511542800

Book DOI: https://doi.org/10.1017/CBO9780511542800
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The representation theory of symmetric groups is one of the most beautiful, popular and important parts of algebra, with many deep relations to other areas of mathematics such as combinatories, Lie theory and algebraic geometry. Kleshchev describes a new approach to the subject, based on the recent work of Lascoux, Leclerc, Thibon, Ariki, Grojnowski and Brundan, as well as his own. Much of this work has previously appeared only in the research literature. However to make it accessible to graduate students, the theory is developed from scratch, the only prerequisite being a standard course in abstract algebra. For the sake of transparency, Kleshchev concentrates on symmetric and spin-symmetric groups, though methods he develops are quite general and apply to a number of related objects. In sum, this unique book will be welcomed by graduate students and researchers as a modern account of the subject.

"The book is written with great care and in a dense style... The author has mastered a very difficult task in writing this book and has enriched the literature on the symmetric groups with a unique and very valuable monograph, making the formidable recent developments more widely accessible by starting the presentation from scratch."
Christine Bessenrodt, Mathematical Reviews

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Linear and Projective Representations of Symmetric Groups

This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

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Contents

Frontmatter
pp i-iv

Contents
pp v-viii

Preface
pp ix-xiv

PART I - LINEAR REPRESENTATIONS
pp 1-2

1 - Notation and generalities
pp 3-6

2 - Symmetric groups I
pp 7-23

3 - Degenerate affine Hecke algebra
pp 24-34

4 - First results on Hn-modules
pp 35-42

5 - Crystal operators
pp 43-53

6 - Character calculations
pp 54-63

7 - Integral representations and cyclotomic Hecke algebras
pp 64-81

8 - Functors eiλ and fiλ
pp 82-102

9 - Construction of Uℤ+ and irreducible modules
pp 103-119

10 - Identification of the crystal
pp 120-130

11 - Symmetric groups II
pp 131-148

PART II - PROJECTIVE REPRESENTATIONS
pp 149-150

12 - Generalities on superalgebra
pp 151-164

13 - Sergeev superalgebras
pp 165-173

14 - Affine Sergeev superalgebras
pp 174-180

15 - Integral representations and cyclotomic Sergeev algebras
pp 181-190

16 - First results on Xn-modules
pp 191-199

17 - Crystal operators for Xn
pp 200-205

18 - Character calculations for Xn
pp 206-218

19 - Operators eiλ and fiλ
pp 219-237

20 - Construction of Uℤ+ and irreducible modules
pp 238-247

21 - Identification of the crystal
pp 248-249

22 - Double covers
pp 250-269

References
pp 270-274

Index
pp 275-277

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Linear and Projective Representations of Symmetric Groups

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