On a Conjecture of Kac-wakimoto
نویسندگان
چکیده
We prove a conjecture about mininmal index of certain representations of Coset Algebraic Conformal Field Theories under certain conditions as formulated previously by us. As a by-product, the Kac-Wakimoto Conjecture (KWC) which is related to the asympotics of the coset characters is true under the same conditions. The same idea in the proof also proves a recent conjecture related to subfactors from conformal inclusions. §
منابع مشابه
Vanishing of Cohomology Associated to Quantized Drinfeld-sokolov Reduction
We prove a vanishing theorem of the cohomology arising from the two quantized Drinfeld-Sokolov reductions (“+” and “−” reduction) introduced by Feigin-Frenkel and Frenkel-Kac-Wakimoto. As a consequence, the vanishing conjecture of Frenkel-Kac-Wakimoto is proved for the “−” reduction and partially for the “+” reduction.
متن کاملRepresentation Theory of Superconformal Algebras and the Kac-roan-wakimoto Conjecture
We study the representation theory of the superconformal algebra Wk(g, fθ) associated to a minimal gradation of g. Here, g is a simple finite-dimensional Lie superalgebra with a non-degenerate even supersymmetric invariant bilinear form. Thus, Wk(g, fθ) can be the Virasoro algebra, the Bershadsky-Polyakov algebra, the Neveu-Schwarz algebra, the BershadskyKnizhnik algebras, the N = 2 superconfor...
متن کاملTwo-sided Bgg Resolutions of Admissible Representations
We prove the conjecture of Frenkel, Kac and Wakimoto on the existence of two-sided BGG resolutions of G-integrable admissible representations of affine Kac-Moody algebras at fractional levels. As an application we establish the semi-infinite analogue of the generalized Borel-Weil theorem for minimal parabolic subalgebras which enables an inductive study of admissible representations.
متن کامل1 6 M ar 1 99 9 ALGEBRAIC COSET CONFORMAL FIELD THEORIES II
Some mathematical questions relating to Coset Conformal field theories (CFT) are considered in the framework of Algebraic Quantum Field Theory as developed previously by us. We consider the issue of fix point resolution in the diagonal coset of type A. We show how to decompose certain reducible representations into irreducibles, and prove that the coset CFT gives rise to a unitary Modular Tenso...
متن کاملOn the Asymptotic Behavior of Kac-wakimoto Characters
Recently, Kac and Wakimoto established specialized character formulas for irreducible highest weight s (m, 1)∧ modules and established a main exponential term in their asymptotic expansions. By different methods, we improve upon the Kac-Wakimoto asymptotics for these characters, obtaining an asymptotic expansion with an arbitrarily large number of terms beyond the main term. More specifically, ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008