"Seminar topics on affine Lie algebras"의 두 판 사이의 차이

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imported>Pythagoras0
 
(다른 사용자 한 명의 중간 판 42개는 보이지 않습니다)
1번째 줄: 1번째 줄:
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Meetings: Thursdays 3-4:30 pm, Priestly Building Seminar Room 67-442
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==memo==
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* http://books.google.com.au/books?id=_0zyWYJGUakC&printsec=frontcover&dq=Application+of+group+theory+in+physics+and+mathematical+physics&source=bl&ots=q5F83jIVbm&sig=ii3X3aeugpTZMFa1DfiGnPOkPSc&hl=en&ei=1FIwTNiXN5SSjAf_0PCWBg&sa=X&oi=book_result&ct=result&redir_esc=y#v=onepage&q&f=false
  
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==topics==
 
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===Kac-Moody algebras===
 
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===affine Lie algerbas as central extensions of loop algerbas===
 
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===Sugawara construction of Virasoro algebra===
 
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===integrable highest weight representations of affine Lie algebras===
 
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===Weyl-Kac character formula and modular transformations===
 
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===fusion rules and Verlinde formula===
 
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===vertex operator constructions of basic representations===
 
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===admissible representations===
 
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* Heisenberg or Virasoro?
 
  
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===future topics===
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==links==
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* admissible representations of affine algebras
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* [https://sites.google.com/site/masoudkomi/research/qft Quantum Field Theory Seminar]
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* Heisenberg algebra
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* W-algebra
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* Feigin-Frenkel isomorphism
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==readings==
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* KZ equation
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* Berman, Stephen, and Karen Hunger Parshall. ‘Victor Kac and Robert Moody: Their Paths to Kac-Moody Lie Algebras’. The Mathematical Intelligencer 24, no. 1 (13 January 2009): 50–60. doi:[http://link.springer.com/article/10.1007%2FBF03025312 10.1007/BF03025312].
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* quantum affine algebra
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* Dolan, Louise. ‘The Beacon of Kac-Moody Symmetry for Physics’. Notices of the American Mathematical Society 42, no. 12 (1995): 1489–95. http://www.ams.org/notices/199512/dolan.pdf
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* Shapovalov form
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* vertex algebra
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* loop groups and positive energy representation
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* free field realization
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** <math>b-c</math> ghost systems
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** <math>\beta-\gamma</math> ghost systems
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** free bosons - Heisenberg
  
  
 
[[분류:Talks and lecture notes]]
 
[[분류:Talks and lecture notes]]
 
[[분류:Lie theory]]
 
[[분류:Lie theory]]
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[[분류:migrate]]

2020년 11월 16일 (월) 04:28 기준 최신판

memo


future topics

  • admissible representations of affine algebras
  • Heisenberg algebra
  • W-algebra
  • Feigin-Frenkel isomorphism
  • KZ equation
  • quantum affine algebra
  • Shapovalov form
  • vertex algebra
  • loop groups and positive energy representation
  • free field realization
    • \(b-c\) ghost systems
    • \(\beta-\gamma\) ghost systems
    • free bosons - Heisenberg
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