{ localUrl: '../page/representation_theory.html', arbitalUrl: 'https://arbital.com/p/representation_theory', rawJsonUrl: '../raw/3tn.json', likeableId: '0', likeableType: 'page', myLikeValue: '0', likeCount: '0', dislikeCount: '0', likeScore: '0', individualLikes: [], pageId: 'representation_theory', edit: '1', editSummary: '', prevEdit: '0', currentEdit: '1', wasPublished: 'true', type: 'wiki', title: 'Representation theory', clickbait: 'The study of how groups act on vector spaces. ', textLength: '941', alias: 'representation_theory', externalUrl: '', sortChildrenBy: 'likes', hasVote: 'false', voteType: '', votesAnonymous: 'false', editCreatorId: 'QiaochuYuan', editCreatedAt: '2016-05-25 22:26:30', pageCreatorId: 'QiaochuYuan', pageCreatedAt: '2016-05-25 22:26:30', seeDomainId: '0', editDomainId: '1025', submitToDomainId: '0', isAutosave: 'false', isSnapshot: 'false', isLiveEdit: 'true', isMinorEdit: 'false', indirectTeacher: 'false', todoCount: '0', isEditorComment: 'false', isApprovedComment: 'true', isResolved: 'false', snapshotText: '', anchorContext: '', anchorText: '', anchorOffset: '0', mergedInto: '', isDeleted: 'false', viewCount: '48', text: '# Advertisement\n\nRepresentation theory (which physicists and chemists sometimes just call [3g8]) is the study of how [3gd groups] $G$ act on [vector_space vector spaces] $V$. A central idea in mathematics is that, because [linear_algebra linear algebra] is so easy (compared to other parts of math), we should always try to extract linear algebra from any situation we can, and representation theory is a standard tool to apply when extracting linear algebra from a situation involving a [3t9]. \n\nIn physics, vector spaces appear naturally as [Hilbert_space Hilbert spaces] of [quantum_state quantum states] associated to physical systems, and representations of groups on these Hilbert spaces appear naturally as symmetries of the system. The study of these representations is a fundamental organizing principle of modern physics; for example, it is behind [Eugene_Wigner Wigner]'s [Wigner_classification classification of particle types]. ', metaText: '', isTextLoaded: 'true', isSubscribedToDiscussion: 'false', isSubscribedToUser: 'false', isSubscribedAsMaintainer: 'false', discussionSubscriberCount: '1', maintainerCount: '1', userSubscriberCount: '0', lastVisit: '', hasDraft: 'false', votes: [], voteSummary: 'null', muVoteSummary: '0', voteScaling: '0', currentUserVote: '-2', voteCount: '0', lockedVoteType: '', maxEditEver: '0', redLinkCount: '0', lockedBy: '', lockedUntil: '', nextPageId: '', prevPageId: '', usedAsMastery: 'false', proposalEditNum: '0', permissions: { edit: { has: 'false', reason: 'You don't have domain permission to edit this page' }, proposeEdit: { has: 'true', reason: '' }, delete: { has: 'false', reason: 'You don't have domain permission to delete this page' }, comment: { has: 'false', reason: 'You can't comment in this domain because you are not a member' }, proposeComment: { has: 'true', reason: '' } }, summaries: {}, creatorIds: [ 'QiaochuYuan' ], childIds: [], parentIds: [], commentIds: [], questionIds: [], tagIds: [], relatedIds: [], markIds: [], explanations: [], learnMore: [], requirements: [], subjects: [], lenses: [], lensParentId: '', pathPages: [], learnMoreTaughtMap: {}, learnMoreCoveredMap: {}, learnMoreRequiredMap: {}, editHistory: {}, domainSubmissions: {}, answers: [], answerCount: '0', commentCount: '0', newCommentCount: '0', linkedMarkCount: '0', changeLogs: [ { likeableId: '0', likeableType: 'changeLog', myLikeValue: '0', likeCount: '0', dislikeCount: '0', likeScore: '0', individualLikes: [], id: '11036', pageId: 'representation_theory', userId: 'QiaochuYuan', edit: '1', type: 'newEdit', createdAt: '2016-05-25 22:26:30', auxPageId: '', oldSettingsValue: '', newSettingsValue: '' } ], feedSubmissions: [], searchStrings: {}, hasChildren: 'false', hasParents: 'false', redAliases: {}, improvementTagIds: [], nonMetaTagIds: [], todos: [], slowDownMap: 'null', speedUpMap: 'null', arcPageIds: 'null', contentRequests: {} }