149 research outputs found
Classification of marked elliptic root systems with non-reduced affine quotient
The class of root systems, called elliptic root systems, were introduced in
1985 by K. Saito, for his studies on a normal surface singularity which
contains a regular elliptic curve in its minimal resolution. He also classified
such root systems when they admit a reduced affine quotient, as root system. In
this note, we provide the classification of elliptic root systems that admit a
non-reduced affine quotient, thus complete the classification of such root
systems.Comment: This is a short annoucement. A detailed (long) version is in
preparatio
Notes on highest weight modules of the elliptic algebra
We discuss a construction of highest weight modules for the recently defined
elliptic algebra , and make several conjectures
concerning them. The modules are generated by the action of the components of
the operator on the highest weight vectors. We introduce the vertex
operators and through their commutation relations with the
-operator. We present ordering rules for the - and -operators and
find an upper bound for the number of linearly independent vectors generated by
them, which agrees with the known characters of -modules.Comment: Nonstandard macro package eliminate
The elliptic quantum algebra and its vertex operators
We construct a realization of the elliptic quantum algebra
for any given level in terms of free boson fields and
their twisted partners. It can be considered as the elliptic deformation of the
Wakimoto realization of the quantum affine algebra . We also
construct a family of screening currents, which commute with the currents of
up to total q-differences. And we give explicit twisted
expressions for the type and the type vertex operators of
by twisting the known results of the type vertex
operators of the quantum affine algebra and the new results
of the type vertex operators of we obtained in this
paper.Comment: 28 page
Super Yangian Double and Its Gauss Decomposition
We extend Yangian double to super (or graded) case and give its Drinfel'd
generators realization by Gauss decomposition.Comment: 6 pages, Latex, no figure
The Virasoro vertex algebra and factorization algebras on Riemann surfaces
This paper focuses on the connection of holomorphic two-dimensional
factorization algebras and vertex algebras which has been made precise in the
forthcoming book of Costello-Gwilliam. We provide a construction of the
Virasoro vertex algebra starting from a local Lie algebra on the complex plane.
Moreover, we discuss an extension of this factorization algebra to a
factorization algebra on the category of Riemann surfaces. The factorization
homology of this factorization algebra is computed as are the correlation
functions. We provide an example of how the Virasoro factorization algebra
implements conformal symmetry of the beta-gamma system using the method of
effective BV quantization
Differential-difference system related to toroidal Lie algebra
We present a novel differential-difference system in (2+1)-dimensional
space-time (one discrete, two continuum), arisen from the Bogoyavlensky's
(2+1)-dimensional KdV hierarchy. Our method is based on the bilinear identity
of the hierarchy, which is related to the vertex operator representation of the
toroidal Lie algebra \sl_2^{tor}.Comment: 10 pages, 4 figures, pLaTeX2e, uses amsmath, amssymb, amsthm,
graphic
On quantum vertex algebras and their modules
We give a survey on the developments in a certain theory of quantum vertex
algebras, including a conceptual construction of quantum vertex algebras and
their modules and a connection of double Yangians and Zamolodchikov-Faddeev
algebras with quantum vertex algebras.Comment: 18 pages; contribution to the proceedings of the conference in honor
of Professor Geoffrey Maso
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