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Topic: Group representation

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	Group representation - Wikipedia, the free encyclopedia
		Group representation theory is the branch of mathematics that studies properties of abstract groups via their representations as linear transformations of vector spaces.
		Representation theory is important because it enables many group-theoretic problems to be reduced to problems in linear algebra, which is a very well-understood theory.
		A representation of a group G on a vector space V over a field K is a group homomorphism from G to GL(V), the general linear group on V.
	en.wikipedia.org /wiki/Group_representation (1365 words)

	Young tableau - Wikipedia, the free encyclopedia
		It provides a convenient way to describe the group representations of the symmetric group and to study their properties.
		Young diagrams are in one-to-one correspondence with irreducible representations of the symmetric group over the complex numbers.
		Young tableaux can be also used to construct representations of the symmetric group over arbitrary fields and to study their structure.
	en.wikipedia.org /wiki/Young_tableau (759 words)

	Group Theory and Physics
		Therefore, the character of the reducible representation is the sum of the characters for the irreducible representations that comprise it.
		The electric dipole moment is a vector, and corresponds to the irreducible representation J = 1 of the rotation group.
		Their representations share many of the properties of the representations of finite groups, but the methods of working with the groups is somewhat different.
	www.du.edu /~jcalvert/phys/groups.htm (5735 words)

	PlanetMath: regular representation (Site not responding. Last check: 2007-11-07)
		Equivalently, the regular representation is the induced representation on
		Cross-references: subgroup, induced representation, linear combinations, vector space, representation, field, group
		This is version 2 of regular representation, born on 2002-02-05, modified 2002-02-05.
	planetmath.org /encyclopedia/RegularRepresentation.html (60 words)

	Unequal Representation: Membership Input and Interest Group Decision-Making (Site not responding. Last check: 2007-11-07)
		When we consider the representational role interest groups play in pluralist, democratic politics, the relative paucity of research on the role of members in the decisions of these groups is striking.
		Variation in membership input within interest groups may be explained by characteristics of the interest group organizations, the reliance of the group on members for financial support, the primary activities performed by the group, or the type of members of which the group is comprised.
		Groups with chapter structures might be thought to facilitate member input better than groups without state or local chapters, providing members with a smaller unit in which to discuss their views and convey them to the leadership.
	www.ksg.harvard.edu /prg/cary/unequal.htm (4957 words)

	GROUP REPRESENTATION THEORY FOR PHYSICISTS
		His research fields are in Group representation theory and its application in physics, hadron physics and computational physics.
		This book introduces systematically the eigenfunction method, a new approach to the group representation theory which was developed by the authors in the 1970's and 1980's in accordance with the concept and method used in quantum mechanics.
		Group Representation Theory for Physicists may serve as a handbook for researchers doing group theory calculations.
	www.worldscibooks.com /physics/5019.html (289 words)

	Standard Group MAC Addresses Tutorial
		The Hexadecimal (in hexadecimal) Representation of LAN MAC addresses have been defined in ISO/IEC 10039 (LAN MAC Service Definition) and are used throughout this document.
		In the Binary Representation the first bit transmitted, of each octet, on the LAN medium is the least significant bit of that octet.
		Group MAC addresses for vendor specific proprietary protocols should be assigned out of the vendor's Universally Administered Address Block.
	standards.ieee.org /regauth/groupmac/tutorial.html (900 words)

	PlanetMath: group representation (Site not responding. Last check: 2007-11-07)
		A representation is faithful if either of the following equivalent conditions is satisfied:
		Cross-references: zero module, property, subspace, injective, equivalent, scalar, structure, homomorphism, equivalence, group ring, module, invertible linear transformations, general linear group, group homomorphism, vector space, group
		This is version 3 of group representation, born on 2002-01-23, modified 2005-01-18.
	planetmath.org /encyclopedia/GroupRepresentation.html (112 words)

	Chapter 3 - The Minkowski Question Mark and the Modular Group (Site not responding. Last check: 2007-11-07)
		This matrix representation of the generators can be used to manipulate and evaluate continued fractions; indeed, the modular group is known as being one way to conveniently work with continued fractions.
		The dyadic and higher-order interval representations are not symplectic.
		Finally, we note that the interval representation is a topology, and that it is not exactly a trivial topology for a subset of the modular group.
	www.linas.org /math/chap-minkowski/chap-minkowski.html (5943 words)

	Exiles - Political, and Philosophical Observations
		The third form is symbolic representation where a group is represented in a more abstract way that is typically historically rooted or traditional (for example, by a monarch or flag).
		Defining women as a group sediments their identities and exaggerates ascribed characteristics leading to an obscuring of the differences between the individual women within the group "women", resulting in a false homogeneity just as oppressive as the wider society.(15) However Phillips also points out that this charge is invalid.
		Therefore it is not the group that is being represented, but the group members.(16) This is achieved by reflecting the diversity of "subject positions" (or differences) within the structure of the group.
	noumenal.net /exiles/representation.html (4523 words)

	AREP: GAP Share Package for Constructive Group Representation Theory (Site not responding. Last check: 2007-11-07)
		By the term "constructive" we mean that group representations are constructed and manipulated up to equality - not only up to equivalence as it is done by using characters.
		A striking application of constructive representation theory is the decomposition of matrices representing discrete signal transforms into a product of highly structured sparse matrices (Examples).
		However, "concrete" would also be right because the representations are given with respect to a fixed basis of the underlying vector space.
	www.ece.cmu.edu /~smart/arep/arep.html (475 words)

	GAP Manual: 61.5 Gain Group Representation (Site not responding. Last check: 2007-11-07)
		In the representation described in section Mathematical Introduction, computing the action of a generator x on a double coset named dk depends on finding the L_x-orbit representative of dk.
		Each gain group L_x is specified by giving an action of K on some domain which is permutationally equivalent to the action of K on left cosets of L_x.
		To allow this, the gain groups are specified as one part of the input, and then another part specifies, for each generator, a reference to the gain group and possibly a conjugating element.
	www-gap.dcs.st-and.ac.uk /oldsite/Manual/C061S005.htm (233 words)

	NEWS FROM COUNCIL - WORKING GROUP ON REPRESENTATION (Site not responding. Last check: 2007-11-07)
		WAC is establishing a working group on representation on the Council and Executive.
		The notion of establishing working groups on topics of particular importance was mooted at WAC-4 during the Executive meeting on Sunday, 9 January 1999.
		Several ideas for working groups were discussed, including the idea of a working group on representation.
	www.wac.uct.ac.za /bulletin/wab9/council4.html (492 words)

	Construction of Group Algebras and their Elements
		Which is most suitable depends on the group G and on the operations required, and must be decided upon when the algebra is created.
		This representation allows group algebras to be defined over any group in which the elements have a canonical form, including potentially infinite matrix groups over a ring of characteristic 0 or even free groups.
		We first construct the default group algebra A = R[G] where R is the ring of integers and G is the symmetric group on three points.
	www.umich.edu /~gpcc/scs/magma/text926.htm (695 words)

	WOST J111 Group Project #1 (Site not responding. Last check: 2007-11-07)
		The group will then make a written presentation to the class interpreting the images and analyzing how gender expectations and images function in the representation the group has chosen.
		The representation of gender that your group chooses may be any number of things or images—advertisements, magazines, a short video clip, a song or a CD, a poster or postcard, a short story or an article, or a greeting card, among others, all of which may be found online.
		Be sure that the representation your group chooses to discuss is something specific—a book, for instance, or a movie is too broad a topic for a representation presentation, although you may choose a scene or specific episode to discuss.
	web.infoave.net /~lrashley/wost/wostgrp1.htm (914 words)

	Database of Simple Groups: Permutations, Presentations, Conjugacy Classes, Maximal Subgroups and Sylow Subgroups
		The representation takes the form of a permutation group representation G, a finite presentation F and isomorphisms phi: F --> G and rho: G --> F (for the larger groups, this map takes some time to compute).
		Given a process P which currently points to a group, return the string describing the maximal subgroups of the group.
		Given a process P which currently points to a group, modify it so that it points to the next group if there is one or make it empty if there is not.
	www.math.uiuc.edu /Software/magma/text77.html (579 words)

	Interest Group Activism & Representation, Spring 2003 Syllabus
		Each group will prepare a lobbying strategy for an issue to be assigned by the professor, and each group will then lobby an elected official (in the context of the simulation only) on the issue.
		We will pay particular attention to differences between groups representing the "nonprofit" sector of the economy and the "profit" sector of the economy.
		Summarize each of the basic theoretical approaches to understanding (1) why interest groups exist, (2) how they are maintained, and (3) what impact they have on public policy.
	ksghome.harvard.edu /~dking/pal-212m-2003.htm (915 words)

	South Brooklyn Legal Services - Group Representation (Site not responding. Last check: 2007-11-07)
		Groups with members, like tenant associations, are eligible if a majority of their members are eligible for our services as individuals and if the group cannot afford to hire a lawyer.
		Groups that provide services, like child care networks that help child care providers, may be eligible for our services if their main function is to assist low-income people and they cannot afford to hire a lawyer.
		We help new groups to establish themselves legally, by incorporating as non profits or obtaining tax exempt status, for example.
	www.sbls.org /grouprep.htm (330 words)

	Delegates' Voice: Sept. 2001 (Site not responding. Last check: 2007-11-07)
		This is a quote from Doug Patchen (Eastern Section representative to the AC for many years), expressing his views at the end of his term.
		Doug's recommendations are to eliminate both the minimum number of members necessary to obtain a seat on the AC and all additional seats for any group, regardless of its number of members.
		To suggest that any councilor needs "back up" is to imply that he or she is incapable of adequately representing the group by him or her self -- something that is patently absurd.
	www.aapg.org /business/hod/2001/09sep/advc.cfm (587 words)

	Presentations (Site not responding. Last check: 2007-11-07)
		Construct a presentation for the permutation group G on a set of strong generators and return the presentation in the form of a finitely presented group F that is isomorphic to G. In Magma, the Todd-Coxeter Schreier algorithm is used to construct the presentation.
		The word group of G is a free group W of rank d.
		Given a permutation group G defined on d generators, return (a) a free group W on d generators represented as a group whose elements are defined by straight-line programs (SLP group), and (b) the homomorphism phi from W to G such that W.i -> G.i, for i = 1,..., d.
	www.umich.edu /~gpcc/scs/magma/text319.htm (471 words)

	The UTEP Knowledge Representation Group
		The Knowledge Representation Group provides an environment for undergraduate and graduate students to learn and to do research together with each other and with the professors.
		The group has a weekly seminar where we review current papers and discuss our own ongoing research.
		For the Spring 2000 semester, the Knowledge Representation Seminar is being held every Wednesday at 10:30 am in CS 222.
	www.cs.utep.edu /csdept/krgroup.html (198 words)

	HMC Applied Representation Theory Group - Projects (Site not responding. Last check: 2007-11-07)
		The Applied Representation Theory Group is currently focusing on decimation-in-frequency fast Fourier transforms, applications of representation theory to voting theory, and the linear complexity of graphs.
		For example, using a decimation-in-frequency approach, we have recently created the fastest known FFT for the important class of symmetric groups for small values of n.
		By using representations of the symmetric group to studying voting, we are working toward the description of a generalized Borda count for elections in which the electorate is asked to rank only a few of their top candidates in an election.
	www.math.hmc.edu /~orrison/art/projects.html (549 words)

	The Hindu Business Line : Pilani AGM held sans MP Birla group representation
		Along with the MP Birla Group, the other major shareholders in Pilani are the GP Birla Group with 25 per cent, BK Birla Group (24 per cent), SK Birla Group (eight per cent) and KK Birla Group (five per cent).
		According to Mr P.K. Khaitan, Director of Pilani Investment, the issue of filling up the vacancy on the board caused by the death of Priyamvada Birla was not discussed at the AGM because it was not the agenda.
		He was supposed to represent the MP Birla Group at the AGM by virtue of his chairmanship of Punjab Produce & Co Ltd, which holds the Pilani Investment shares.
	www.thehindubusinessline.com /2004/09/30/stories/2004093001470200.htm (386 words)

	Gabor Wavelets and the Heisenberg Group
		The paper provides a bridge between the engineering and signal processing terminology and group representation theory.
		It is the main goal of this paper to show how the abstract theory of coorbit spaces as developed in a series of papers by Feichtinger-Gröchenig, as described in Banach spaces related to integrable group representations and their atomic decompositions, I.
		In particular a proof of the kernel theorem is given, which also plays a big role in Quantization of TF lattice-invariant operators on elementary LCA groups (Feichtinger-Kozek Chapter of the Gabor Book 1998).
	www.mat.univie.ac.at /~nuhag/papers/1992/fgr1192.html (302 words)

	WOST J111 Group Project Guidelines
		This object should display a cultural representation of gender, female, male, or both genders represented together; the image may also deal with socioeconomic class or with race in addition to gender.
		The representation of gender that your group chooses may be any number of things or images--advertisements, magazines, a short video clip, a song or a CD, a poster or postcard, a short story or an article, or a greeting card, among others, all of which may be found online.
		Be sure that the representation your group chooses to discuss is something specific--a book, for instance, or a movie is too broad a topic for a representation presentation, although you may choose a scene or specific episode to discuss.
	web.infoave.net /~lrashley/111grpassgn.htm (848 words)

	Singapore - Hutchinson encyclopedia article about Singapore
		The constitution of 1965, amended in 1991, provides for a one-chamber parliament, whose 81 members are elected for five-year terms by universal suffrage from 40 single-member wards, two ‘non-constituency’ seats (with restricted voting rights), intended for opposition candidates, and, from 1988, 13 three-member Group Representation Constituencies (GRC) through a simple plurality system.
		In October 1996 parliament passed bills that would improve representation of minority races, including ethnic Indians and Malays.
		In the general election of January 1997 the ruling PAP, led by prime minister Goh Chok Tong, reversed its recent slide in support and captured 65% of the vote (up 4% on 1991) and 81 seats in the 83-member parliament.
	encyclopedia.farlex.com /Singapore (1581 words)

	CDISC Standards
		The Trial Design Subteam of the PR Group and SDS Team has released Part 2 of the Trial Design Model (TDM) for comment.
		The ICH E6 guidance identifies certain essential documents that are required for the conduct of a clinical trial and may supplement the clinical trial protocol.
		This Protocol Supplements list is posted together with the "Protocol Elements" document so that reviewers familiar with the various documents that are frequently part of trial planning and execution can see clearly which are included in the protocol itself and which ones are typically attached to protocols as supplements.
	www.cdisc.org /standards/protocol.html (413 words)

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