On the Modular Representations of the Symmetric Group

1942 ◽  
Vol 43 (4) ◽  
pp. 656 ◽  
Author(s):  
R. M. Thrall ◽  
C. J. Nesbitt
Keyword(s):  
Symmetric Group ◽  
Modular Representations

On the Modular Representations of the Symmetric Group

1954 ◽  
Vol 6 ◽  
pp. 486-497 ◽  
Author(s):  
G. de B. Robinson
Keyword(s):  
Representation Theory ◽  
Symmetric Group ◽  
Young Diagram ◽  
Modular Representation ◽  
Modular Representations ◽  
Modular Representation Theory

The study of the modular representation theory of the symmetric group has been greatly facilitated lately by the introduction of the graph (9, III ), the q-graph (5) and the hook-graph (4) of a Young diagram [λ]. In the present paper we seek to coordinate these ideas and relate them to the r-inducing and restricting processes (9, II ).

scholarly journals Modular Representations of Sn

1964 ◽  
Vol 16 ◽  
pp. 191-203 ◽  
Author(s):  
G. de B. Robinson
Keyword(s):  
Representation Theory ◽  
Symmetric Group ◽  
Modular Representations ◽  
Modular Theory ◽  
Definition Of ◽  
Image Position

The purpose of this paper is to clarify and sharpen the argument in the last two chapters of the author's Representation theory of the symmetric group(3). When these chapters were written the peculiar properties of the case p = 2 were not fully appreciated. No difficulty arises in the definition of the block in terms of the p-core, or in the application of the general modular theory based on the formula

scholarly journals Irreducible Modular Representations of the Reflection GroupG(m,1,n)

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
José O. Araujo ◽  
Tim Bratten ◽  
Cesar L. Maiarú
Keyword(s):  
Symmetric Group ◽  
Weyl Group ◽  
Reflection Group ◽  
Geometric Construction ◽  
Weyl Groups ◽  
Modular Representations ◽  
Complex Reflection ◽  
Complex Reflection Group ◽  
One Year ◽  
Combinatorial Methods

In an article published in 1980, Farahat and Peel realized the irreducible modular representations of the symmetric group. One year later, Al-Aamily, Morris, and Peel constructed the irreducible modular representations for a Weyl group of typeBn. In both cases, combinatorial methods were used. Almost twenty years later, using a geometric construction based on the ideas of Macdonald, first Aguado and Araujo and then Araujo, Bigeón, and Gamondi also realized the irreducible modular representations for the Weyl groups of typesAnandBn. In this paper, we extend the geometric construction based on the ideas of Macdonald to realize the irreducible modular representations of the complex reflection group of typeG(m,1,n).

scholarly journals ON THE MODULAR REPRESENTATIONS OF THE SYMMETRIC GROUP VI

1955 ◽  
Vol 41 (8) ◽  
pp. 596-598
Author(s):  
G. De B. Robinson ◽  
O. E. Taulbee
Keyword(s):  
Symmetric Group ◽  
Modular Representations ◽  
Group Vi

On p-quotients and star diagrams of the symmetric group

1953 ◽  
Vol 49 (1) ◽  
pp. 157-160 ◽  
Author(s):  
H. Farahat
Keyword(s):  
Symmetric Group ◽  
Modular Representations

The star diagram of a diagram [λ] was first obtained by Robinson (5) who denned and studied it, thus giving a unique characterization of the hook structure of [λ]. Staal (6) continued Robinson's work and obtained some important results. Recently, Littlewood (2) published a paper on the modular representations of the symmetric group in which he defined ‘congruent partitions’, ‘p-quotients’, etc., relating to the diagram [λ]. Littlewood's ideas, though superficially different from those of Robinson and Staal, are in essence equivalent to them.

Modular Representations of the Symmetric Group

1951 ◽  
Vol 3 ◽  
pp. 309-327 ◽  
Author(s):  
J. H. Chung
Keyword(s):  
Symmetric Group ◽  
The Other ◽  
Modular Representations ◽  
Young Diagrams ◽  
Starting Point ◽  
The One ◽  
The Relationship

The theory of modular representations of the symmetric group was studied first by Nakayama (5, 6), and later by Thrall and Nesbitt (11) and Robinson (7, 8, 9). Nakayama built up his elaborate theory of hooks for the express purpose of studying this problem, while Robinson's extensive work on the various phases of the relationship between Young diagrams, skew diagrams and star diagrams on the one hand, and representations of the symmetric group on the other, culminating in a set of relations among the degrees of the representations, serves as a starting point for this paper.

Hall–Littlewood polynomials at roots of 1 and modular representations of the symmetric group

1991 ◽  
Vol 110 (3) ◽  
pp. 443-453 ◽  
Author(s):  
A. O. Morris ◽  
N. Sultana
Keyword(s):  
Symmetric Group ◽  
Modular Representations ◽  
Littlewood Polynomials ◽  
Infinite Set

We first give a brief introduction to Hall–Littlewood functions; we follow closely the notation used in Macdonald [3].Let λ = (λ1,…,λm) be a be a partition of n; that is λ1 + … + λm = n, λ1 ≥ λ2 ≥ … ≥ λm >0. We shall sometimes write l(λ) for m and refer to l(λ) as the length of λ and we shall write |λ| for ∑λi. Let x1, x2, … be an infinite set of indeterminates and t an indeterminate independent of the xi (i = 1,2, …). Let Pλ(x;t) = Pλ(x1, x2, …t) and Qλ(x,t) = Qλ(xl, x2, …t) be the Hall–Littlewood P- and Q-functions defined as in Macdonald.

scholarly journals On Self-Mullineux and Self-Conjugate Partitions

10.37236/9283 ◽  
2021 ◽  
Vol 28 (1) ◽  
Author(s):  
Ana Bernal
Keyword(s):  
Symmetric Group ◽  
Fixed Points ◽  
Alternating Group ◽  
Modular Representations ◽  
Distinguished Subset

The Mullineux involution is a relevant map that appears in the study of the modular representations of the symmetric group and the alternating group. The fixed points of this map  are certain partitions of particular interest. It is known that the cardinality of the set of these self-Mullineux partitions is equal to the cardinality of a distinguished subset of self-conjugate partitions. In this work, we give an explicit bijection between the two families of partitions in terms of the Mullineux symbol.

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