scholarly journals Universal induced characters and restriction rules for the classical groups

1990 ◽  
Vol 117 ◽  
pp. 173-205 ◽  
Author(s):  
Yasuo Teranishi
Keyword(s):  
Representation Theory ◽  
Symmetric Group ◽  
Linear Group ◽  
General Linear Group ◽  
Hilbert Series ◽  
Point Of View ◽  
Classical Groups ◽  
Starting Point ◽  
Definition Of ◽  
Matrix Invariants

The purpose of this paper is the study of some basic properties of universal induced characters and their applications to the representation theory of the classical groups (for the definition of a universal induced character, see § 3).The starting point was the paper [F] by E. Formanek on matrix invariants. In his paper [F], Formanek has investigated the Hilbert series for the ring of matrix invariants from the point of view of the representation theory of the general linear group and the symmetric group. In this paper we shall study polynomial concomitants of a group from the same point of view.

scholarly journals SCURTĂ INCURSIUNE ÎN LUMEA LITERARĂ A SCRIITORILOR CONTEMPORANI ROMÂNI DE EXPRESIE SPANIOLĂ

2021 ◽  
pp. 238-255
Author(s):  
Ioana CECOVNIUC ◽  
Keyword(s):  
Point Of View ◽  
Distinctive Features ◽  
Starting Point ◽  
Definition Of ◽  
Significant Factors

The aim of this paper is to briefly review the work of three contemporary Romanian poets from an ectopic point of view. Consequently, the starting point will be from Tomás Albaladejo Mayordomo’s definition of “ectopic literature” (2011), seen as the literature that is produced by an author who changes his usual topos (physical, socio-cultural and linguistic background) for an initially odd or peculiar one. Distinctive features of “ectopic literature” as well as significant factors - such as autobiographical data and main themes - are earmarked to be applied to the work for subsequent analysis.

Sustainable urban land use: Definition, theoretical basis and review of morphology aspect concepts

2009 ◽  
Vol 1 (2) ◽  
pp. 153-170
Author(s):  
Ranka Gajić
Keyword(s):  
Land Use ◽  
Theoretical Basis ◽  
Urban Land ◽  
Urban Land Use ◽  
Point Of View ◽  
Theory And Practice ◽  
Urban Planner ◽  
Starting Point ◽  
Definition Of ◽  
Spatial Entities

The topic of sustainable urban land use compared to the world theory and practice has almost not been elaborated by the professionals in Serbia. This paper's starting point is that it is important to analyze and apply this topic, not only for the master plan level but also for the more detailed levels of planning and for smaller spatial entities/complexes in the cities, focusing on the morphological implications of sustainable urban land use as the topic relevant from the architect/urban planner point of view. After the definition of the notion of sustainable urban land use and the theoretical basis has been defined in the introductory explications, followed by a brief review of that topic's presence in Serbia, the point of view has been explained - namely, focusing on one single aspect (morphology) followed by a review of relevant criteria of other aspects of sustainable urban land use (economical, ecological and social aspects). The conclusion derived by synthesis represents the recommendation for a possible practice/methodology for planner's approach to the sustainable urban land use from the viewpoint of the morphology aspect.

Induced Representations and Invariants

1950 ◽  
Vol 2 ◽  
pp. 334-343 ◽  
Author(s):  
G. DE B. Robinson
Keyword(s):  
Representation Theory ◽  
Symmetric Group ◽  
Explicit Formula ◽  
Linear Group ◽  
Schur Functions ◽  
The Other ◽  
Induced Representations ◽  
Direct Sum ◽  
Invariant Matrices ◽  
The One

1. Introduction. The problem of the expression of an invariant matrix of an invariant matrix as a direct sum of invariant matrices is intimately associated with the representation theory of the full linear group on the one hand and with the representation theory of the symmetric group on the other. In a previous paper the author gave an explicit formula for this reduction in terms of characters of the symmetric group. Later J. A. Todd derived the same formula using Schur functions, i.e. characters of representations of the full linear group.

scholarly journals Free subgroups in maximal subgroups of skew linear groups

2019 ◽  
Vol 29 (03) ◽  
pp. 603-614 ◽  
Author(s):  
Bui Xuan Hai ◽  
Huynh Viet Khanh
Keyword(s):  
Linear Group ◽  
Division Ring ◽  
General Linear Group ◽  
Subnormal Subgroup ◽  
Free Subgroup ◽  
Maximal Subgroups ◽  
Linear Groups ◽  
Locally Finite ◽  
Starting Point ◽  
Free Subgroups

The study of the existence of free groups in skew linear groups have begun since the last decades of the 20th century. The starting point is the theorem of Tits (1972), now often referred to as Tits’ Alternative, stating that every finitely generated subgroup of the general linear group [Formula: see text] over a field [Formula: see text] either contains a non-cyclic free subgroup or it is solvable-by-finite. In this paper, we study the existence of non-cyclic free subgroups in maximal subgroups of an almost subnormal subgroup of the general skew linear group over a locally finite division ring.

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

A Remark by Philip Hall

1958 ◽  
Vol 1 (1) ◽  
pp. 21-23 ◽  
Author(s):  
G. de B. Robinson
Keyword(s):  
Representation Theory ◽  
Symmetric Group ◽  
Linear Group ◽  
Characteristic Zero ◽  
Irreducible Representations ◽  
Young Diagrams ◽  
Linear Transformations ◽  
Modern Physics ◽  
The Right ◽  
The Relationship

The relationship between the representation theory of the full linear group GL(d) of all non-singular linear transformations of degree d over a field of characteristic zero and that of the symmetric group Sn goes back to Schur and has been expounded by Weyl in his classical groups, [4; cf also 2 and 3]. More and more, the significance of continuous groups for modern physics is being pressed on the attention of mathematicians, and it seems worth recording a remark made to the author by Philip Hall in Edmonton.As is well known, the irreducible representations of Sn are obtainable from the Young diagrams [λ]=[λ1, λ2 ,..., λr] consisting of λ1 nodes in the first row, λ2 in the second row, etc., where λ1≥λ2≥ ... ≥λr and Σ λi = n. If we denote the jth node in the ith row of [λ] by (i,j) then those nodes to the right of and below (i,j), constitute, along with the (i,j) node itself, the (i,j)-hook of length hij.

scholarly journals Constructing projective varieties in weighted flag varieties II

2015 ◽  
Vol 158 (2) ◽  
pp. 193-209 ◽  
Author(s):  
MUHAMMAD IMRAN QURESHI
Keyword(s):  
Linear Group ◽  
Lie Group ◽  
General Linear Group ◽  
Hilbert Series ◽  
Flag Variety ◽  
General Linear ◽  
Flag Varieties ◽  
Projective Varieties

AbstractWe give the construction of weighted Lagrangian GrassmannianswLGr(3,6) and weighted partialA3flag varietywFL1,3coming from the symplectic Lie group Sp(6, ℂ) and the general linear group GL(4, ℂ) respectively. We give general formulas for their Hilbert series in terms of Lie theoretic data. We use them as key varieties (Format) to construct some families of polarized 3-folds in codimension 7 and 9. Finally, we list all the distinct weighted flag varieties in codimension (4 ⩽c⩽ 10.

scholarly journals Branching from the General Linear Group to the Symmetric Group and the Principal Embedding

2021 ◽  
Vol 4 (2) ◽  
pp. 189-200
Author(s):  
Alexander Heaton ◽  
Songpon Sriwongsa ◽  
Jeb F. Willenbring
Keyword(s):  
Symmetric Group ◽  
Linear Group ◽  
General Linear Group ◽  
General Linear
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