24,306 research outputs found
On the endomorphisms of Weyl modules over affine Kac-Moody algebras at the critical level
We present an independent short proof of the main result of arXiv:0706.3725
that the algebra of endomorphisms of a Weyl module of critical level is
isomorphic to the algebra of functions on the space of monodromy-free opers on
the disc with regular singularity and residue determined by the highest weight
of the Weyl module. We derive this from the results of arXiv:0712.1183 about
the shift of argument subalgebras.Comment: 9 page
New observables in topological instantonic field theories
Instantonic theories are quantum field theories where all correlators are
determined by integrals over the finite-dimensional space (space of generalized
instantons). We consider novel geometrical observables in instantonic
topological quantum mechanics that are strikingly different from standard
evaluation observables. These observables allow jumps of special type of the
trajectory (at the point of insertion of such observables).
They do not (anti)commute with evaluation observables and raise the dimension
of the space of allowed configurations, while the evaluation observables lower
this dimension. We study these observables in geometric and operator
formalisms. Simple examples are explicitly computed; they depend on linking of
the points.
The new "arbitrary jump" observables may be used to construct correlation
functions computing e.g. the linking numbers of cycles, as we illustrate on
Hopf fibration.Comment: 16 pages, accepted to Journal of Geometry and Physic
Representations of certain non-rational vertex operator algebras of affine type
In this paper we study a series of vertex operator algebras of integer level
associated to the affine Lie algebra . These vertex operator
algebras are constructed by using the explicit construction of certain singular
vectors in the universal affine vertex operator algebra at the
integer level. In the case or , we explicitly determine Zhu's
algebras and classify all irreducible modules in the category . In
the case , we show that the vertex operator algebra contains
two linearly independent singular vectors of the same conformal weight.Comment: 15 pages, LaTeX; final version, to appear in J. Algebr
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