Lectures on conformal field theory and related topics

Speaker: Akihiro Tsuchiya
Title: Extended W algebra of type A.D.E. at positive rational level
Date (JST): Sat, May 26, 2012, 15:30 - 17:30
Place: Seminar Room A
Abstract: For each simple Lie algebra g and complex number k, an infinite dimensional algebra called W algebra, W_k(g) were defined and has been studied by many physicists and mathematicians. They have very complicated algebraic structure and are discussed by the language of Vertex operator algebras (V.O.A.). When g is sl_2(C), it gives the Virasoro algebra.
Recently the representation theory of these algebras are interested by many mathematicians and physicists.
I have been studied in the case of k= p_-/p_+ positive rational level, and g is of type A.D.E. Quite recently I got concrete results. In these cases I found that these V.O.A. W_k(g) can be extended in a larger V.O.A. M_{p_+,p_-}(g). They are defined by compactified free bosono and screening operators. These V.O.A. M_{p_+,p_-}(g) has very nice structure and can be concretely analyzed.
In this talk, I will give their fundamental properties (some are conjectures).
Remarks: Akihiro Tsuchiya was a starting member of IPMU in mathemtics and has been a principal investigator in mathematics 2008-2011. He retired from IPMU in March 2012. We thank him for his contributions to start mathematics at IPMU. We plan to have his last lecture at IPMU as follows. All are welcome.

Date: May 26 (Sat), 2012
Place: Seminar Room A, IPMU

13:30 - 15:00 Yoshitake Hashimoto (Tokyo City Univ.)
15:00 - 15:30 Tea break
15:30 - 17:30 Akihiro Tsuchiya
18:00 - Dinner