Ramond sector of superconformal algebras via quantum reduction

Quantum hamiltonian reduction of affine superalgebras is studied in the twisted case. The Ramond sector of "minimal" superconformal W-algebras is described in detail, the determinant formula is obtained. Extensive list of examples includes all the simple Lie superalgebras of rank up to 2. The paper generalizes the results of Kac and Wakimoto (math-ph/0304011) to the twisted case.Comment: 50 pages, 8 figures; v2: examples added, determinant formula derivation modified, section order change

W_{1+\infty} and W(gl_N) with central charge N

We study representations of the central extension of the Lie algebra of differential operators on the circle, the W-infinity algebra. We obtain complete and specialized character formulas for a large class of representations, which we call primitive; these include all quasi-finite irreducible unitary representations. We show that any primitive representation with central charge N has a canonical structure of an irreducible representation of the W-algebra W(gl_N) with the same central charge and that all irreducible representations of W(gl_N) with central charge N arise in this way. We also establish a duality between "integral" modules of W(gl_N) and finite-dimensional irreducible modules of gl_N, and conjecture their fusion rules.Comment: 29 pages, Latex, uses file amssym.def (a few remarks added, typos corrected

Fusion and singular vectors in A1{(1)} highest weight cyclic modules

We show how the interplay between the fusion formalism of conformal field theory and the Knizhnik--Zamolodchikov equation leads to explicit formulae for the singular vectors in the highest weight representations of A1{(1)}.Comment: 42 page

Classification of finite irreducible modules over the Lie conformal superalgebra CK6

We classify all continuous degenerate irreducible modules over the exceptional linearly compact Lie superalgebra E(1, 6), and all finite degenerate irreducible modules over the exceptional Lie conformal superalgebra CK6, for which E(1, 6) is the annihilation algebra

Characters of (relatively) integrable modules over affine Lie superalgebras

In the paper we consider the problem of computation of characters of relatively integrable irreducible highest weight modules L over finite-dimensional basic Lie superalgebras and over affine Lie superalgebras g. The problem consists of two parts. First, it is the reduction of the problem to the [bar over g]-module F(L), where [bar over g] is the associated to L integral Lie superalgebra and F(L) is an integrable irreducible highest weight [bar over g]-module. Second, it is the computation of characters of integrable highest weight modules. There is a general conjecture concerning the first part, which we check in many cases. As for the second part, we prove in many cases the KW-character formula, provided that the KW-condition holds, including almost all finite-dimensional g-modules when g is basic, and all maximally atypical non-critical integrable g-modules when g is affine with non-zero dual Coxeter number.Simons Foundation. Postdoctoral Fellowshi

Classification of linearly compact simple Nambu-Poisson algebras

We introduce the notion of a universal odd generalized Poisson superalgebra associated with an associative algebra A, by generalizing a construction made in the work of De Sole and Kac [Jpn. J. Math. 8, 1\u2013145 (2013)]. By making use of this notion we give a complete classification of simple linearly compact (generalized) n-Nambu-Poisson algebras over an algebraically closed field of characteristic zero

Supersymmetric vertex algebras

We define and study the structure of SUSY Lie conformal and vertex algebras. This leads to effective rules for computations with superfields.Comment: 71 page

Denominator identities for finite-dimensional Lie superalgebras and Howe duality for compact dual pairs

We provide formulas for the denominator and superdenominator of a basic classical type Lie superalgebra for any set of positive roots. We establish a connection between certain sets of positive roots and the theory of reductive dual pairs of real Lie groups. As an application of our formulas, we recover the Theta correspondence for compact dual pairs. Along the way we give an explicit description of the real forms of basic classical type Lie superalgebras.Comment: Latex, 75 pages. Minor corrections. Final version, to appear in the Japanese Journal of Mathematic

Generalized Drinfeld-Sokolov Hierarchies II: The Hamiltonian Structures

In this paper we examine the bi-Hamiltonian structure of the generalized KdV-hierarchies. We verify that both Hamiltonian structures take the form of Kirillov brackets on the Kac-Moody algebra, and that they define a coordinated system. Classical extended conformal algebras are obtained from the second Poisson bracket. In particular, we construct the $W_n^l$ algebras, first discussed for the case $n=3$ and $l=2$ by A. Polyakov and M. Bershadsky.Comment: 41 page