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Quasifinite highest weight modules over the Lie algebra of differential operators on the circle
AbstractWe classify positive energy representations with finite degeneracies of the Lie algebraW1+∞ and construct them in terms of representation theory of the Lie algebra $$\hat gl(\infty ,R_m )$$
Representation theory of the vertex algebraW1+∞
In our paper [KR] we began a systematic study of representations of the universal central extension of the Lie algebra of differential operators on the circle. This study was continued in the paper
W_1+∞ and W(gl_N) with central charge N
The Lie algebra D̂, which is the unique non-trivial central extension of the Lie algebra D of differential operators on the circle [KP1], has appeared recently in various models of two-dimensional
A family of poisson structures on hermitian symmetric spaces
We investigate the compatibility of symplectic Kirillov-Kostant-Souriau structure and Poisson-Lie structure on coadjoint orbits of semisimple Lie group. We prove that they are compatible for an orbit
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
Representation theory of the vertex algebra $W_{1 + \infty}$
In our paper~\cite{KR} we began a systematic study of representations of the universal central extension $\widehat{\Cal D}\/$ of the Lie algebra of differential operators on the circle. This study
Noncommutative differential geometry related to the Young-Baxter equation
An analogue of the differential calculus associated with a unitary solution of the quantum Young-Baxter equation is constructed. An example of a ring sheaf is considered in which local solutions of
Generalized internal long waves equations: Construction, Hamiltonian structure, and conservation laws
A general class of the ILW type equations is constructed. We introduce a Hamiltonian structure and construct an infinite number of conservation laws.
Poisson Structure for Restricted Lie Algebras
The Poisson bracket is an important invariant of a deformation of a commutative associative algebra A (cf. [D]). Given a family of associative (but not necessarily commutative) algebras Ah, such that
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