"Ring of symmetric functions"의 두 판 사이의 차이

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structure on ring of symmetric functions S
  
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# commutative algebra
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# cocommutative coalgebra
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# antipode involutions
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# symmetric bilinear form <,> algebra structure dual to coalgebra structure
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# partial order \geq
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# lots of bases
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1,2,3 => commutative, cocommutative Hopf algebra, coordinate ring of a commutative group scheme
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S\otimes \mathbb{Q} is UEA of a Lie algebra
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list of places where algebra S of symmetric functions turns up
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(1) ring of symmetric functions
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(2) representation theory of symmetric group S_n
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(3) representation theory of general linear group Gl_n
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(4) homology of BU (classifying space for vector bundles)
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(5) Cohomology of Grassmannians
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(6) Schubert calculus
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(7) universal \lambda ring on 1-generator
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(8) coordinate ring of group scheme of power series 1+e_1x+e_2x^2+\cdots
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(9) Hall algebra of finite abelian p-groups
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(10) Polynomial functors of vector spaces
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(11) underlying space of algebra of Bosons in 1-dim
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==related items==
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* [[Hall algebra]]
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[[분류:migrate]]
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==메타데이터==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q17102788 Q17102788]
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===Spacy 패턴 목록===
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* [{'LOWER': 'ring'}, {'LOWER': 'of'}, {'LOWER': 'symmetric'}, {'LEMMA': 'function'}]

2021년 2월 17일 (수) 02:41 기준 최신판

structure on ring of symmetric functions S


  1. commutative algebra
  2. cocommutative coalgebra
  3. antipode involutions
  4. symmetric bilinear form <,> algebra structure dual to coalgebra structure
  5. partial order \geq
  6. lots of bases


1,2,3 => commutative, cocommutative Hopf algebra, coordinate ring of a commutative group scheme



S\otimes \mathbb{Q} is UEA of a Lie algebra


list of places where algebra S of symmetric functions turns up

(1) ring of symmetric functions

(2) representation theory of symmetric group S_n

(3) representation theory of general linear group Gl_n

(4) homology of BU (classifying space for vector bundles)

(5) Cohomology of Grassmannians

(6) Schubert calculus

(7) universal \lambda ring on 1-generator

(8) coordinate ring of group scheme of power series 1+e_1x+e_2x^2+\cdots

(9) Hall algebra of finite abelian p-groups

(10) Polynomial functors of vector spaces

(11) underlying space of algebra of Bosons in 1-dim


related items

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'ring'}, {'LOWER': 'of'}, {'LOWER': 'symmetric'}, {'LEMMA': 'function'}]
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