1,721,034 research outputs found
W-algebras in type A and the Arakawa-Moreau conjecture
No full textW-algebras are an important class of vertex algebras associated with a reductive Lie algebra g, a nilpotent element f ∈ g and a scalar k ∈ C, which are closely related with various area of mathematics such as integrable systems, two-dimensional conformal field theories, modular representation theory, four dimensional gauge theory, and geometric Langlands program. Moreover, there has been a renewed interest in W-algebras since they appear as invariants of Argyres-Douglas theory via the 4D/2D correspondence recently discovered in physics. However, despite of the importance of W-algebras the problem of finding all the generators for every affine W-algebra remains unsolved. The only results known so far are from Kac-Wakimoto for minimal nilpotent elements, and from Arakawa-Molev for rectangular nilpotent elements, with the restriction of g = glN. In this thesis we obtained an explicit list of generators of W-algebras of type A associated with quasi-rectangular nilpotent elements. This is a nice generalization of the aforementioned results, since both are quasi-rectangular. Furthermore, as an application we were able to confirm a conjecture of Anne Moreau and Tomoyuki Arakawa in some cases on the isomorphism of simple quotients of W-algebras. This is a promising result since it confirms also some expectations by physicists that arose in the recent study of the 4D/2D correspondence
Singular degree of a rational matrix pseudodifferential operator
No full textIn our previous work we studied minimal fractional decompositions of a rational matrix pseudodifferential operator: H=A/B, where A and B are matrix differential operators, and B is non-degenerate of minimal possible degree deg(B). In the present paper we introduce the singular degree sdeg(H)=deg(B), and show that for an arbitrary rational expression H=sum_a (A^a_1)/(B^a_1)...(A^a_n)/(B^a_n), we have that sdeg(H) is less than or equal to sum_{a,i} deg(B^a_i). If the equality holds, we call such an expression minimal. We study the properties of the singular degree and of minimal rational expressions. These results are important for the computations involved in the Lenard-Magri scheme of integrability
Structure of classical (finite and affine) W-algebras
Full text linkFirst, we derive an explicit formula for the Poisson bracket of the classical finite W- Algebra Wfin(g, f), the algebra of polynomial functions on the Slodowy slice associated to a simple Lie algebra g and its nilpotent element f . On the other hand, we produce an explicit set of generators and we derive an explicit formula for the Poisson vertex algebra structure of the classical affine W- Algebra W(g, f). As an immediate consequence, we obtain a Poisson algebra isomorphism between Wfin(g, f) and the Zhu algebra of W(g, f).We also study the generalized Miura map for classicalW- Algebras
Conformal embeddings and simple current extensions
Full text linkIn this paper we investigate the structure of intermediate vertex algebras associated with a maximal conformal embedding of a reductive Lie algebra in a semisimple Lie algebra of classical type
Decomposition rules for conformal pairs associated to symmetric spaces and abelian subalgebras of \Bbb Z\sb 2-graded Lie algebras.
No full textABSTRACT:We give uniform formulas for the branching rules of level 1 modules over orthogonal affine Lie algebras for all conformal pairs associated to symmetric spaces. We also provide a combinatorial interpretation of these formulas in terms of certain abelian subalgebras of simple Lie algebras. © 2006 Elsevier Inc. All rights reserved
Multiplets of representations, twisted Dirac operators and Vogan's conjecture in affine setting
No full textABSTRACT: We extend classical results of Kostant et al. on multiplets of representations of finite-dimensional Lie algebras and on the cubic Dirac operator to the setting of affine Lie algebras and twisted affine cubic Dirac operator. We prove in this setting an analogue of Vogan's conjecture on infinitesimal characters of Harish-Chandra modules in terms of Dirac cohomology. For our calculations we use the machinery of Lie conformal and vertex algebras. © 2007 Elsevier Inc. All rights reserved
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