"Ring of symmetric functions"의 두 판 사이의 차이
Pythagoras0 (토론 | 기여) |
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| (사용자 3명의 중간 판 17개는 보이지 않습니다) | |||
| 1번째 줄: | 1번째 줄: | ||
| − | structure on ring of symmetric functions | + | structure on ring of symmetric functions S |
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# commutative algebra | # commutative algebra | ||
| 10번째 줄: | 10번째 줄: | ||
# lots of bases | # lots of bases | ||
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1,2,3 => commutative, cocommutative Hopf algebra, coordinate ring of a commutative group scheme | 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 | 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== | ||
| + | * [[Hall algebra]] | ||
| + | [[분류:migrate]] | ||
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| + | ==메타데이터== | ||
| + | ===위키데이터=== | ||
| + | * ID : [https://www.wikidata.org/wiki/Q17102788 Q17102788] | ||
| + | ===Spacy 패턴 목록=== | ||
| + | * [{'LOWER': 'ring'}, {'LOWER': 'of'}, {'LOWER': 'symmetric'}, {'LEMMA': 'function'}] | ||
2021년 2월 17일 (수) 01:41 기준 최신판
structure on ring of symmetric functions S
- commutative algebra
- cocommutative coalgebra
- antipode involutions
- symmetric bilinear form <,> algebra structure dual to coalgebra structure
- partial order \geq
- 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
메타데이터
위키데이터
- ID : Q17102788
Spacy 패턴 목록
- [{'LOWER': 'ring'}, {'LOWER': 'of'}, {'LOWER': 'symmetric'}, {'LEMMA': 'function'}]