W-algebras – introduction, screenings and quantum groups

Lecture 3 Boris FEIGIN

Course Description
Sometimes people use the words vertex operator algebra and W-algebra as synonyms. This is partly correct, but not entirely. Theory of W-algebras is a collection of extremely interesting examples of new algebraic objects and theory of vertex algebra is an attempt to understand and find some order in this zoo. Our lectures are the introduction – so we concentrate on examples and simplest methods of constructing the W-algebras. Note that W-algebras are deeply connected with 2-dimensional conformal field theory. So it is not possible to talk about W-algebras and do not mention some facts from the algebraic geometry of the curves. This short course consists of an introduction to random dynamical systems, from a predominantly geometric point of view. The aim is to introduce basic concepts in the context of simple examples. We will discuss some elementary results and highlight open questions.
1. Clifford algebra, Lattice vertex operator algebras.
2. Coinvariants and vertex operators.
3. Subalgebras in lattice vertex algebras. Screenings. Quantum groups and screenings.
4. Fermionic screenings. Algebra 01.png on a critical level.
5. Deformation of universal enveloping of the Lie algebra of differential operators on the circle.
6. Plane partitions and W-algebras. (something about recent progress)

講義詳細

年度・期
2017年度・前期集中
開催日
2017年7月10日 から 7月14日
開講部局名
理学研究科
使用言語
英語
教員/講師名
Boris FEIGIN(Distinguished Visiting Professor, Kyoto University / Professor, Higher School of Economics)
開催場所
Room 127, Graduate School of Science Bldg No 3
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