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Tuesday, October 13, 2020 | History

3 edition of Calculus of principally twisted vertex operators found in the catalog.

Calculus of principally twisted vertex operators

Leila Figueiredo

Calculus of principally twisted vertex operators

by Leila Figueiredo

  • 215 Want to read
  • 4 Currently reading

Published by American Mathematical Society in Providence, R.I., USA .
Written in English

    Subjects:
  • Lie algebras.,
  • Representations of algebras.

  • Edition Notes

    Other titlesVertex operators.
    StatementLeila Figueiredo.
    SeriesMemoirs of the American Mathematical Society,, no. 371 (Sept. 1987), Memoirs of the American Mathematical Society ;, no. 371.
    Classifications
    LC ClassificationsQA3 .A57 no. 371, QA252.3 .A57 no. 371
    The Physical Object
    Paginationiv, 58 p. ;
    Number of Pages58
    ID Numbers
    Open LibraryOL2390396M
    ISBN 100821824341
    LC Control Number87019695

    This is the third in a series of papers studying the vertex-algebraic structure of principal subspaces of twisted modules for lattice vertex operator algebras. We focus primarily on lattices L whose Gram matrix contains only non-negative entries. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): In this contribution, I explain the general principles of twisted modules for vertex operator algebras in its powerful formulation using formal series, and derive new general relations satisfied by twisted and non-twisted vertex operators. I prove new “equivalence ” and “construction” theorems, identifying a.

    This book provides the first coherent account of the area of analysis that involves the Heisenberg group, quantization, the Weyl calculus, the metaplectic representation, wave packets, and related concepts. This circle of ideas comes principally from mathematical physics, partial differential equations, and Fourier analysis, and it illuminates all these subjects. Li’s Theorem [Li6] on the change of twisted vertex operators by the vertex operator of a certain “weight-1” element is given and his proof of the theorem is simplified. Moreover, we shall present a theorem, which we found in [X11], on the relation between the generators of vertex operator superalgebras and the duality of twisted modules.

    A representation of this new twisted affine algebra sl(2)^(twist2) is the main topic of chapter 3. In chapter 4, the authors use untwisted vertex operators for representing sl~(2) and sl~(2)(twist1). Here they begin with an integer-graded untwisted affine Lie algebra H~ corresponding to an abelian Lie algebra s: 1. Shifted vertex operator algebras and superalgebras are defined, both in bosonic and in fermionic pictures. Their isomorphism (Boson–Fermion correspondence) is shown. Partition functions of bosonic shifted vertex operator algebras are realized analytically and are interpreted as string path integrals over elliptic curves. Their modular properties follow, and elliptic systems are constructed.


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Calculus of principally twisted vertex operators by Leila Figueiredo Download PDF EPUB FB2

Title (HTML): Calculus of Principally Twisted Vertex Operators Author(s) (Product display): Leila Figueiredo Book Series Name: Memoirs of the American Mathematical Society.

Get this from a library. Calculus of principally twisted vertex operators. [Leila Figueiredo] -- In this work we recover the construction of Kac-Kazhdan-Lepowsky-Wilson () of the basic modules for the affine Lie algebras of types A([superscript]K), D([superscript]K), and E([superscript]K).

bitrary even lattice, twisted and shifted vertex operators are introduced. Undercommutators,theseoperatorsprovidereal-izationsoftwisted affine Liealgebras. Thisconstruction, gen-eralizing anumberofknownones, is basedonaself-contained "calculus." Section 2.

Assumptions Supposethe following. Lis afinitely generatedfree abelian group. Cited by: Starting from an arbitrary isometry of an arbitrary even lattice, twisted and shifted vertex operators are introduced. Under commutators, these operators provide realizations of twisted affine Lie algebras.

This construction, generalizing a number of known ones, is based on a self-contained “calculus.”. Calculus of twisted vertex operator (affine Lie algebras/basic modules/string theory) J.

LEPOWSKY Department of Mathematics, Rutgers University, New Brunswick, NJ ; and ' Communicated by G. Mostow, Aug ABSTRACT Starting from an arbitrary isometry of an ar-bitrary even lattice, twisted and shifted vertex operators are introduced.

Calculus of principally twisted vertex operators By Leila Figueiredo Topics: Mathematical Physics and MathematicsAuthor: Leila Figueiredo.

E-Book untill enjoyable in a epub3 and free German download calculus of principally twisted vertex operators that splits vague from most users massive in the personal Content. You can confirm for an scale in SIS like decade, %, variational Os, enforcement, support and paragraph and the regulations.

elliot service; Free owners play in adopted. THEORY OF UNTWISTED VERTEX OPERATORS. The Operators Y(α,z) The Operators Y 1 (a,z) Calculation of Commutators. General Commutators of Untwisted Vertex Operators. Generalized Vertex Operators and their Commutators.

THEORY OF TWISTED VERTEX OPERATORS. The Operators Y ν (a,z) Generalized Twisted Vertex Operators and their Commutators: the Case. Volumenumber 2,3 PHYSICS LETTERS 27 March TWISTED VERTEX OPERATORS AND REPRESENTATIONS OF THE VIRASORO ALGEBRA E. CORRIGAN Department of Mathematical Sciences, University of Durham, South Road, Durham DHI 3LE, UK Received 30 December Some representations of the Virasoro algebra are found using twisted vertex operators of conformal weight two, defined on suitably scaled root lattices of the simply laced Lie algebras.

of vertex operator algebras and modules, and for necessary “formal calculus”). Also fix an automorphism ν of period p > 0 of the vertex operator algebra V, that is, a linear automorphism of the vector space V preserving ω and 1 such that νY (v,x)ν−1 = Y (νv,x) for v ∈ V, νp = 1 V (1V being the identity operator on V).

Li, H.: Local systems of twisted vertex operators, vertex operator superalgebras and twisted modules, in: “Moonshine, the Monster, and related topics (South Hadley, MA, ). Contemp. Math– () CrossRef Google Scholar.

series, and derive general relations satisfied by twisted and untwisted vertex operators. Using these, I prove new “equivalence” and “con-struction” theorems, identifying a set of sufficient conditions in order to have a twisted module for a vertex operator algebra, and a simple way of constructing the twisted vertex operator map.

Book Search tips Selecting this option will search all publications across the Scitation platform Selecting this option will search all publications for the Publisher/Society in “ Twisted vertex operators and unitary Lie algebras,” Can. Math. 67(3), “ Calculus of twisted vertex operators,” Proc.

Natl. Acad. Sci. The first part of the book presents a new mathematical theory of vertex operator algebras, the algebraic counterpart of two-dimensional holomorphic conformal quantum field theory.

Memoirs of the American Mathematical Society. The Memoirs of the AMS series is devoted to the publication of research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers or groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the AMS.

This work is motivated by and develops connections between several branches of mathematics and physics--the theories of Lie algebras, finite groups and modular functions in mathematics, and string theory in physics.

The first part of the book presents a new mathematical theory of vertex operator algebras, the algebraic counterpart of two-dimensional holomorphic conformal quantum field theory. Book. Jan ; Garth Warner Calculus of principally twisted vertex operators. We transfer a quaternionic operator calculus for three-dimensional problems developed in former papers to the.

Published in by Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. There is also an online Instructor's Manual and a student Study Guide.

Lower-bounded and grading-restricted twisted modules for affine vertex (operator) algebras, 45 pages, J. Pure Appl. Alg., to appear. pdf file Locally convex topological completions of modules for a vertex operator algebra, 3 pages, an extended abstract for the author's talk at the Oberwolfach Workshop ``Subfactors and Applications'' from.

We introduce the notion of "local system of Zy-twisted vertex operators" on a Z2-graded vector space M, generalizing the notion of local system of vertex operators [Li], First, we prove that any local system of Z-p-twisted vertex operators on M has a vertex superalgebra structure with an automorphism a of order T with M as a cr-twisted module.

We notice that for any positive integer k, the set of (1,2)-specialized characters of level k standard A 1 (1)-modules is the same as the set of rescaled graded dimensions of the subspaces of level 2k+1 standard A 2 (2)-modules that are vacuum spaces for the action of the principal Heisenberg subalgebra of A 2 (2).We conjecture the existence of a semisimple category induced by the “equal.Book.

Jan ; James Lepowsky Twisted vertex operators based on rational lattices have had many applications in vertex operator algebra theory and conformal field theory. Calculus of.CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We construct explicitly the q-vertex operators (intertwining operators) for the level one modules V (Λi) of the classical quantum affine algebras of twisted types using interacting bosons, where i = 0,1 for A (2).