2 edition of **Modular representations of the symmetric group** found in the catalog.

Modular representations of the symmetric group

J. H. Chung

- 360 Want to read
- 40 Currently reading

Published
**1950**
by s.n.] in [Toronto
.

Written in English

**Edition Notes**

Thesis (Ph.D.)--University of Toronto, 1950.

Statement | J. H. Chung. |

ID Numbers | |
---|---|

Open Library | OL14848944M |

Irreducible Representations of the Symmetric Group. Extension of the Ground Field. Group Characters. Modular Representations. Introduction. On group rings over a modular field which possess radicals expressible as principal ideals, Sci. For the sake of transparency, Kleshschev concentrates on symmetric and spin-symmetric groups, though the 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 › Books › Science & Math › Mathematics.

The p-Modular Descent Algebra of the Symmetric Group Article (PDF Available) in Bulletin of the London Mathematical Society 29(04) July with 12 Reads How we measure 'reads' The Representation Theory of the Symmetric Group provides an account of both the ordinary and modular representation theory of the symmetric groups. The range of applications of this theory is vast, varying from theoretical physics, through combinatories to the study of polynomial identity algebras; and new uses are still being ://

Abstract: In this paper we prove theorems that describe how the representation theory of the affine Hecke algebra of type A and of related algebras such as the group algebra of the symmetric group are controlled by integrable highest weight representations of the characteristic zero affine Lie algebra \hat{sl}_l. In particular we parameterise the representations of these algebras by the nodes Questions about modular representation theory of finite groups can often be reduced to elementary abelian subgroups. This is the first book to offer a detailed study of the representation theory of elementary abelian groups, bringing together information from many papers and journals, as well as unpublished ://

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Modular Representations of Symmetric Groups Charlotte Chan Sunday, August 7, nis the symmetric group, the set of permutations on nobjects. We pick n2N[f0gsuch that char(K) = p ~charchan/ Among these codes arising from 2-modular irreducible representations of symmetric groups, there are—besides the trivially optimal codes and the codes for which the minimal distance is not yet available for reasons of computer power—the distance optimal binary codes with the parameter triples (n,k,d) equal to (9,4,4) and (14,8,4):// Full text Full text is available as a scanned copy of the original print version.

Get a printable copy (PDF file) of the complete article (K), or click on a page image below to browse page by page. Links to PubMed are also available for Selected :// Introduction It is a well known fact that for a given prime p the p-modular irreducible representations D of the symmetric group S n of degree n are labelled in a canonical way by the p-regular Modular representations of symmetric groups.

View/ Open. (Mb) Date Author. Levenstein, Dustan. Share Facebook Twitter LinkedIn. Metadata Show full item record. Abstract. I have studied representation theory of finite groups, in particular of the symmetric group over fields of prime characteristics. Over C On the Modular Representations of the General Linear and Symmetric Groups Roger W.

Carter Modular representations of the symmetric group book George Lusztig 1. Introduction This paper is the result of our attempt to extend the classical theory of polynomial representations of the general linear group GL, (~;) and~baumeist/sommerschule/ The p-residue and p-quotient of a partition are defined, and a formula is obtained relating to symmetric group characteristics.

A procedure is described whereby the mode of separation in every case may be determined, of the 0-characters of the symmetric groups into :// Modular Representations (Classical) At the character level: 1, 2 are in the same block if there is a chain 1, 11, 2 such that any two consecutive characters have a Brauer character in common when reduced mod p.

Bhama Srinivasan (University of Illinois at Chicago) Modular Representations Regina, May 9 / ~srinivas/ The symmetric group S(n) plays a fundamental role in mathematics. It arises in all sorts of di erent contexts, so its importance can hardly be over-stated.

There are thousands of pages of research papers in mathematics journals which involving this group in one way or another. We have al-ready seen from Cayley’s theorem that every nite group ~carrell/ 1. Representations of the symmetric group Let nbe a positive integer, S nthe symmetric group on f1;;ngand FS nthe group algebra over the eld F.

We remind that if Gis a group then the group algebra FGis the vector space over F with basis G, and the multiplication in FGis given by extending the multiplication in G. The representation theory of ~peresi/ Modular irreducible representations of the symmetric group as linear codes Adalbert Kerber, Axel Kohnert Lehrstuhl II f¨ur Mathematik, University of Bayreuth, D Bayreuth, Germany Accepted 10 October Available online 13 January F¨ur Alain, in herzlicher Freundschaft Abstract An earlier reference for the minimality of these degrees over any field is n, Representations of the general symmetric group as linear groups in finite and infinite fields, Trans.

Amer. Math. Soc. 9 (), This can be found in Dickson's Collected :// Brauer R, Nesbitt C. On the Regular Representations of Algebras. Proc Natl Acad Sci U S A. Apr; 23 (4)– [PMC free article] Robinson G de B. On the Modular Representations of the Symmetric Group (III).

Proc Natl Acad Sci U S A. May; 38 (5)– [PMC free article] thereby giving representations of the group on the homology groups of the space. If there is torsion in the homology these representations require something other than ordinary character theory to be understood.

This book is written for students who are studying nite group representation theory beyond the level of a rst course in abstract ~webb/RepBook/ On The Modular Representations of the Symmetric Group.

Proc Natl Acad Sci U S A. Oct; 37 (10)– [ PMC free article ] [ PubMed ] [ Google Scholar ] Abstract. We describe a particularly easy way of evaluating the modular irreducible matrix representations of the symmetric group.

It shows that Specht's approach to the ordinary irreducible representations, along Specht polynomials, can be unified with Clausen's approach to the modular irreducible representations using symmetrized standard ?doi= The first half of this book contains the text of the first edition of LNM volumePolynomial Representations of GL classic account of matrix representations, the Schur algebra, the modular representations of GL n, and connections with symmetric groups, has been the basis of much research in representation theory.

The second half is an Appendix, and can be read independently of the There are two approaches to projective representation theory of symmetric and alternating groups, which are powerful enough to work for modular representations.

One is based on Sergeev duality, which connects projective representation theory of the symmetric group and representation theory of the algebraic supergroup \(Q(n)\) via appropriate =memo From the reviews of the second edition: "This work is an introduction to the representation theory of the symmetric group.

Unlike other books on the subject this text deals with the symmetric group from three different points of view: general representation theory, combinatorial algorithms and symmetric functions. › Mathematics › Algebra. This book provides the first concise and self-contained introduction to the theory on the simplest yet very nontrivial example of the infinite symmetric group, focusing on its deep connections to probability, mathematical physics, and algebraic › Books › Science & Math › Mathematics.

determine all the 2-modular representations of any particular symmetric group. In the cases we consider, the 2-modular irreducible character turning up from an ordinary character x is found to be the modular character of a module, whose 2-modular character is On the Modular Representations of the Symmetric Group (III).

(PMID PMCID:PMC) Full Text Citations ; BioEntities ; Related Articles ; External Links ; Proc Natl Acad Sci U S A. May; 38(5): – PMCID: PMC On the Modular Representations of the Symmetric Group (III) G.

de B. Robinson Author information Low-dimensional irreducible 2-modular representations of the symmetric group I apologize if this question is a little too basic for MathOverflow, but it's somewhat outside of my background and I'm frustrated that the answer doesn't seem to be explicit in the literature even