710 research outputs found
Finite growth representations of infinite Lie conformal algebras
We classify all finite growth representations of all infinite rank
subalgebras of the Lie conformal algebra gc_1 that contain a Virasoro
subalgebra.Comment: 22 page
Irreducible modules over finite simple Lie conformal superalgebras of type K
We construct all finite irreducible modules over Lie conformal superalgebras
of type KComment: Accepted for publication in J. Math. Phys
Highest weight irreducible representations of the Lie superalgebra
Two classes of irreducible highest weight modules of the general linear Lie
superalgebra are constructed. Within each module a basis is
introduced and the transformation relations of the basis under the action of
the algebra generators are written down.Comment: 24 pages, TeX; Journ. Math. Phys. (to be published
Open Systems Viewed Through Their Conservative Extensions
A typical linear open system is often defined as a component of a larger
conservative one. For instance, a dielectric medium, defined by its frequency
dependent electric permittivity and magnetic permeability is a part of a
conservative system which includes the matter with all its atomic complexity. A
finite slab of a lattice array of coupled oscillators modelling a solid is
another example. Assuming that such an open system is all one wants to observe,
we ask how big a part of the original conservative system (possibly very
complex) is relevant to the observations, or, in other words, how big a part of
it is coupled to the open system? We study here the structure of the system
coupling and its coupled and decoupled components, showing, in particular, that
it is only the system's unique minimal extension that is relevant to its
dynamics, and this extension often is tiny part of the original conservative
system. We also give a scenario explaining why certain degrees of freedom of a
solid do not contribute to its specific heat.Comment: 51 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
Random matrices with external source and KP functions
In this paper we prove that the partition function in the random matrix model
with external source is a KP function.Comment: 12 pages, title change
On indecomposable modules over the Virasoro algebra
It is proved that an indecomposable Harish-Chandra module over the Virasoro
algebra must be (i) a uniformly bounded module, or (ii) a module in Category
, or (iii) a module in Category , or (iv) a module which
contains the trivial module as one of its composition factors.Comment: 5 pages, Latex, to appear in Science in China
Highest weight representations of the quantum algebra U_h(gl_\infty)
A class of highest weight irreducible representations of the quantum algebra
U_h(gl_\infty) is constructed. Within each module a basis is introduced and the
transformation relations of the basis under the action of the Chevalley
generators are explicitly written.Comment: 7 pages, PlainTe
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