"Springer correspondence"의 두 판 사이의 차이
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==introduction== | ==introduction== | ||
| + | * In his paper [Spr76], Springer defined a certain representation of the Weyl group of a reductive group on the cohomology of a set of fixed points in the flag variety by a nilpotent element, which we now call the Springer representation. | ||
| + | * In particular, for various sets of such fixed points, called Springer fibers, the top degree cohomology gives all the irreducible representations of the corresponding Weyl group. | ||
* The Springer correspondence makes a link between the characters of a Weyl group and the geometry of the nilpotent cone of the corresponding semisimple Lie algebra | * The Springer correspondence makes a link between the characters of a Weyl group and the geometry of the nilpotent cone of the corresponding semisimple Lie algebra | ||
* extend this to an equivalence between the triangulated category generated by the Springer perverse sheaves and the derived category of differential graded modules over a dg-ring related to the Weyl group | * extend this to an equivalence between the triangulated category generated by the Springer perverse sheaves and the derived category of differential graded modules over a dg-ring related to the Weyl group | ||
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| + | ==nilpotent variety== | ||
| + | * Given a semisimple algebraic group <math>G</math> with Lie algebra <math>\mathfrak{g}</math>, we call the closure of a <math>G</math>-orbit in the nilpotent elements of <math>\mathfrak{g}</math> a nilpotent variety. | ||
| + | |||
| + | ==related items== | ||
| + | * {{수학노트|url=콕세터_군의_표현론}} | ||
==expositions== | ==expositions== | ||
| + | * Achar, Pramod N., Anthony Henderson, Daniel Juteau, and Simon Riche. “Modular Generalized Springer Correspondence: An Overview.” arXiv:1510.08962 [math], October 29, 2015. http://arxiv.org/abs/1510.08962. | ||
* Clausen, http://www.math.harvard.edu/theses/senior/clausen/clausen.pdf | * Clausen, http://www.math.harvard.edu/theses/senior/clausen/clausen.pdf | ||
| + | |||
| + | ==encyclopedia== | ||
| + | * http://en.wikipedia.org/wiki/Nilpotent_cone | ||
| + | * http://en.wikipedia.org/wiki/Springer_correspondence | ||
==articles== | ==articles== | ||
| + | * Julianna Tymoczko, The geometry and combinatorics of Springer fibers, arXiv:1606.02760 [math.AG], June 08 2016, http://arxiv.org/abs/1606.02760 | ||
| + | * Aubert, Anne-Marie, Ahmed Moussaoui, and Maarten Solleveld. “Generalizations of the Springer Correspondence and Cuspidal Langlands Parameters.” arXiv:1511.05335 [math], November 17, 2015. http://arxiv.org/abs/1511.05335. | ||
| + | * Chen, Tsao-Hsien, Kari Vilonen, and Ting Xue. “Hessenberg Varieties, Intersections of Quadrics, and the Springer Correspondence.” arXiv:1511.00617 [math], November 2, 2015. http://arxiv.org/abs/1511.00617. | ||
| + | * Achar, Pramod N., Anthony Henderson, Daniel Juteau, and Simon Riche. “Modular Generalized Springer Correspondence III: Exceptional Groups.” arXiv:1507.00401 [math], July 1, 2015. http://arxiv.org/abs/1507.00401. | ||
* Juteau, Daniel. “Modular Springer Correspondence, Decomposition Matrices and Basic Sets.” arXiv:1410.1471 [math], October 6, 2014. http://arxiv.org/abs/1410.1471. | * Juteau, Daniel. “Modular Springer Correspondence, Decomposition Matrices and Basic Sets.” arXiv:1410.1471 [math], October 6, 2014. http://arxiv.org/abs/1410.1471. | ||
* Rider, Laura, and Amber Russell. “Perverse Sheaves on the Nilpotent Cone and Lusztig’s Generalized Springer Correspondence.” arXiv:1409.7132 [math], September 24, 2014. http://arxiv.org/abs/1409.7132. | * Rider, Laura, and Amber Russell. “Perverse Sheaves on the Nilpotent Cone and Lusztig’s Generalized Springer Correspondence.” arXiv:1409.7132 [math], September 24, 2014. http://arxiv.org/abs/1409.7132. | ||
* Rider, Laura. “Formality for the Nilpotent Cone and a Derived Springer Correspondence.” arXiv:1206.4343 [math], June 19, 2012. http://arxiv.org/abs/1206.4343. | * Rider, Laura. “Formality for the Nilpotent Cone and a Derived Springer Correspondence.” arXiv:1206.4343 [math], June 19, 2012. http://arxiv.org/abs/1206.4343. | ||
| + | * Ciubotaru, Dan. “Spin Representations of Weyl Groups and the Springer Correspondence.” Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal) 2012, no. 671 (2011): 199–222. doi:10.1515/CRELLE.2011.160. | ||
| + | * Springer, T.A.. "Trigonometric Sums, Green Functions on Finite Groups and Representation of Weyl Groups.." Inventiones mathematicae 36 (1976): 173-208 | ||
| + | ** http://ams.mpim-bonn.mpg.de/mathscinet-getitem?mr=MR0442103 | ||
| + | [[분류:duality]] | ||
| + | [[분류:Lie theory]] | ||
| + | [[분류:migrate]] | ||
| − | + | ==메타데이터== | |
| − | + | ===위키데이터=== | |
| − | + | * ID : [https://www.wikidata.org/wiki/Q7580874 Q7580874] | |
| − | == | + | ===Spacy 패턴 목록=== |
| − | * | + | * [{'LOWER': 'springer'}, {'LEMMA': 'correspondence'}] |
| − | * | ||
2021년 2월 17일 (수) 02:01 기준 최신판
introduction
- In his paper [Spr76], Springer defined a certain representation of the Weyl group of a reductive group on the cohomology of a set of fixed points in the flag variety by a nilpotent element, which we now call the Springer representation.
- In particular, for various sets of such fixed points, called Springer fibers, the top degree cohomology gives all the irreducible representations of the corresponding Weyl group.
- The Springer correspondence makes a link between the characters of a Weyl group and the geometry of the nilpotent cone of the corresponding semisimple Lie algebra
- extend this to an equivalence between the triangulated category generated by the Springer perverse sheaves and the derived category of differential graded modules over a dg-ring related to the Weyl group
nilpotent variety
- Given a semisimple algebraic group \(G\) with Lie algebra \(\mathfrak{g}\), we call the closure of a \(G\)-orbit in the nilpotent elements of \(\mathfrak{g}\) a nilpotent variety.
expositions
- Achar, Pramod N., Anthony Henderson, Daniel Juteau, and Simon Riche. “Modular Generalized Springer Correspondence: An Overview.” arXiv:1510.08962 [math], October 29, 2015. http://arxiv.org/abs/1510.08962.
- Clausen, http://www.math.harvard.edu/theses/senior/clausen/clausen.pdf
encyclopedia
articles
- Julianna Tymoczko, The geometry and combinatorics of Springer fibers, arXiv:1606.02760 [math.AG], June 08 2016, http://arxiv.org/abs/1606.02760
- Aubert, Anne-Marie, Ahmed Moussaoui, and Maarten Solleveld. “Generalizations of the Springer Correspondence and Cuspidal Langlands Parameters.” arXiv:1511.05335 [math], November 17, 2015. http://arxiv.org/abs/1511.05335.
- Chen, Tsao-Hsien, Kari Vilonen, and Ting Xue. “Hessenberg Varieties, Intersections of Quadrics, and the Springer Correspondence.” arXiv:1511.00617 [math], November 2, 2015. http://arxiv.org/abs/1511.00617.
- Achar, Pramod N., Anthony Henderson, Daniel Juteau, and Simon Riche. “Modular Generalized Springer Correspondence III: Exceptional Groups.” arXiv:1507.00401 [math], July 1, 2015. http://arxiv.org/abs/1507.00401.
- Juteau, Daniel. “Modular Springer Correspondence, Decomposition Matrices and Basic Sets.” arXiv:1410.1471 [math], October 6, 2014. http://arxiv.org/abs/1410.1471.
- Rider, Laura, and Amber Russell. “Perverse Sheaves on the Nilpotent Cone and Lusztig’s Generalized Springer Correspondence.” arXiv:1409.7132 [math], September 24, 2014. http://arxiv.org/abs/1409.7132.
- Rider, Laura. “Formality for the Nilpotent Cone and a Derived Springer Correspondence.” arXiv:1206.4343 [math], June 19, 2012. http://arxiv.org/abs/1206.4343.
- Ciubotaru, Dan. “Spin Representations of Weyl Groups and the Springer Correspondence.” Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal) 2012, no. 671 (2011): 199–222. doi:10.1515/CRELLE.2011.160.
- Springer, T.A.. "Trigonometric Sums, Green Functions on Finite Groups and Representation of Weyl Groups.." Inventiones mathematicae 36 (1976): 173-208
메타데이터
위키데이터
- ID : Q7580874
Spacy 패턴 목록
- [{'LOWER': 'springer'}, {'LEMMA': 'correspondence'}]