Carina Boyallian

Quasifinite highest weight modules over the Lie algebra of matrix differential operators on the circle

We classify positive energy representations with finite degeneracies of the Lie algebraW1+∞ and construct them in terms of representation theory of the Lie algebra\(\hat gl(\infty ,R_m )\) of infinites matrices with finite number of non-zero diagonals over the algebraR m =ℂ[t]/(tm+1). The unitary ones are classified as well. Similar results are obtained for the sin-algebras.

Finite growth representations of infinite Lie conformal algebras

We classify all finite growth representations of all infinite rank subalgebras of the Lie conformal algebra gc1 that contain a Virasoro subalgebra.

Matrix-valued bispectral operators and quasideterminants

We consider a matrix-valued version of the bispectral problem, that is, find differential operators and with matrix coefficients such that there exists a family of matrix-valued common eigenfunctions ψ(x, z): where f and Θ are matrix-valued functions. Using quasideterminants, we prove that the operators L obtained by non-degenerated rational matrix Darboux transformations from are bispectral operators, where and D is a diagonal matrix. We also give a procedure to find an explicit formula for the operator B extending previous results in the scalar case.

Representations of simple finite Lie conformal superalgebras of type W and S

We construct all finite irreducible modules over Lie conformal superalgebras of type W and S.

Classification of finite irreducible modules over the Lie conformal superalgebra CK 6

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 superalgebra.

Representations of a symplectic type subalgebra of W∞N

In this paper we classify the irreducible quasifinite highest weight modules over the symplectic type Lie subalgebra of the Lie algebra of all regular differential operators on circle that kill constants. We also realize them in terms of the representations theory of the complex Lie algebra gl∞[m] of infinite matrices with a finite number of non-zero diagonals with entries in the algebra of truncated polynomials and the corresponding subalgebras of type C.

Irreducible modules over finite simple Lie conformal superalgebras of type K

We construct all finite irreducible modules over Lie conformal superalgebras of type K.We construct all finite irreducible modules over Lie conformal superalgebras of type K.

Lie Subalgebras of the Matrix Quantum Pseudodifferential Operators

We give a complete description of the anti-involutions that preserve the principal gradation of the algebra of matrix quantum pseudodifferential operators and we describe the Lie subalgebras of its minus fixed points.

The Central Extension Defining the Super Matrix Generalization of

We prove that the Lie superalgebra of regular differential operators on the superspace has an essentially unique non-trivial central extension.