2,968 research outputs found
Kazhdan-Lusztig tensoring and Harish-Chandra categories
We use the Kazhdan-Lusztig tensoring to define affine translation functors,
describe annihilating ideals of highest weight modules over an affine Lie
algebra in terms of the corresponding VOA, and to sketch a functorial approach
to ``affine Harish-Chandra bimodules''.Comment: 22 pages late
Vertex Lie algebras and cyclotomic coinvariants
Electronic version of an article published as Benoît Vicedo and Charles Young, Commun. Contemp. Math. 0, 1650015 (2016) [62 pages] DOI: http://dx.doi.org/10.1142/S0219199716500152 Vertex Lie algebras and cyclotomic coinvariants.Given a vertex Lie algebra equipped with an action by automorphisms of a cyclic group , we define spaces of cyclotomic coinvariants over the Riemann sphere. These are quotients of tensor products of smooth modules over `local' Lie algebras assigned to marked points , by the action of a `global' Lie algebra of -equivariant functions. On the other hand, the universal enveloping vertex algebra of is itself a vertex Lie algebra with an induced action of . This gives `big' analogs of the Lie algebras above. From these we construct the space of `big' cyclotomic coinvariants, i.e. coinvariants with respect to . We prove that these two definitions of cyclotomic coinvariants in fact coincide, provided the origin is included as a marked point. As a corollary we prove a result on the functoriality of cyclotomic coinvariants which we require for the solution of cyclotomic Gaudin models in arXiv:1409.6937. At the origin, which is fixed by , one must assign a module over the stable subalgebra of . This module becomes a -quasi-module in the sense of Li. As a bi-product we obtain an iterate formula for such quasi-modules.Peer reviewe
Meromorphic open-string vertex algebras
A notion of meromorphic open-string vertex algebra is introduced. A
meromorphic open-string vertex algebra is an open-string vertex algebra in the
sense of Kong and the author satisfying additional rationality (or
meromorphicity) conditions for vertex operators. The vertex operator map for a
meromorphic open-string vertex algebra satisfies rationality and associativity
but in general does not satisfy the Jacobi identity, commutativity, the
commutator formula, the skew-symmetry or even the associator formula. Given a
vector space \mathfrak{h}, we construct a meromorphic open-string vertex
algebra structure on the tensor algebra of the negative part of the
affinization of \mathfrak{h} such that the vertex algebra struture on the
symmetric algebra of the negative part of the Heisenberg algebra associated to
\mathfrak{h} is a quotient of this meromorphic open-string vertex algebra. We
also introduce the notion of left module for a meromorphic open-string vertex
algebra and construct left modules for the meromorphic open-string vertex
algebra above.Comment: 43 pape
Vertex-algebraic structure of the principal subspaces of certain A_1^(1)-modules, I: level one case
This is the first in a series of papers in which we study vertex-algebraic
structure of Feigin-Stoyanovsky's principal subspaces associated to standard
modules for both untwisted and twisted affine Lie algebras. A key idea is to
prove suitable presentations of principal subspaces, without using bases or
even ``small'' spanning sets of these spaces. In this paper we prove
presentations of the principal subspaces of the basic A_1^(1)-modules. These
convenient presentations were previously used in work of
Capparelli-Lepowsky-Milas for the purpose of obtaining the classical
Rogers-Ramanujan recursion for the graded dimensions of the principal
subspaces.Comment: 20 pages. To appear in International J. of Mat
Constructing quantum vertex algebras
This is a sequel to \cite{li-qva}. In this paper, we focus on the
construction of quantum vertex algebras over \C, whose notion was formulated
in \cite{li-qva} with Etingof and Kazhdan's notion of quantum vertex operator
algebra (over \C[[h]]) as one of the main motivations. As one of the main
steps in constructing quantum vertex algebras, we prove that every
countable-dimensional nonlocal (namely noncommutative) vertex algebra over
\C, which either is irreducible or has a basis of PBW type, is nondegenerate
in the sense of Etingof and Kazhdan. Using this result, we establish the
nondegeneracy of better known vertex operator algebras and some nonlocal vertex
algebras. We then construct a family of quantum vertex algebras closely related
to Zamolodchikov-Faddeev algebras.Comment: 37 page
Free Boson Representation of
A representation of the quantum affine algebra of an
arbitrary level is constructed in the Fock module of eight boson fields.
This realization reduces the Wakimoto representation in the
limit. The analogues of the screening currents are also obtained. They commute
with the action of modulo total differences of some
fields.Comment: 12 pages, LaTeX, RIMS-920, YITP/K-101
The Dirac Sea
We give an alternate definition of the free Dirac field featuring an explicit
construction of the Dirac sea. The treatment employs a semi-infinite wedge
product of Hilbert spaces. We also show that the construction is equivalent to
the standard Fock space construction.Comment: 7 page
Non Abelian Sugawara Construction and the q-deformed N=2 Superconformal Algebra
The construction of a q-deformed N=2 superconformal algebra is proposed in
terms of level 1 currents of quantum affine
Lie algebra and a single real Fermi field. In particular, it suggests the
expression for the q-deformed Energy-Momentum tensor in the Sugawara form. Its
constituents generate two isomorphic quadratic algebraic structures. The
generalization to is also proposed.Comment: AMSLATEX, 21page
Jacobi Identity for Vertex Algebras in Higher Dimensions
Vertex algebras in higher dimensions provide an algebraic framework for
investigating axiomatic quantum field theory with global conformal invariance.
We develop further the theory of such vertex algebras by introducing formal
calculus techniques and investigating the notion of polylocal fields. We derive
a Jacobi identity which together with the vacuum axiom can be taken as an
equivalent definition of vertex algebra.Comment: 35 pages, references adde
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