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Structure of the Standard Modules for the Affine Lie Algebra \(A^{(1)}_1\)
James Lepowsky and Mirko Primc
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Contemporary Mathematics
1985; 84 pp; softcover
Volume: 46
ISBN-10: 0-8218-5048-2
ISBN-13: 978-0-8218-5048-0
List Price: US$25
Member Price: US$20
Order Code: CONM/46
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The affine Kac-Moody algebra \(A_1^{(1)}\) has recently served as a source of new ideas in the representation theory of infinite-dimensional affine Lie algebras. In particular, several years ago it was discovered that \(A_1^{(1)}\) and then a general class of affine Lie algebras could be constructed using operators related to the vertex operators of the physicists' string model. This book develops the calculus of vertex operators to solve the problem of constructing all the standard \(A_1^{(1)}\)-modules in the homogeneous realization.

Aimed primarily at researchers in and students of Lie theory, the book's detailed and concrete exposition makes it accessible and illuminating even to relative newcomers to the field.

Table of Contents

  • The Lie algebra \(A_1^(1)\)
  • The category \(\cal P_k\)
  • The generalized commutation relations
  • Relations for standard modules
  • Basis of \(\Omega_L\) for a standard module \(L\)
  • Schur functions
  • Proof of linear independence
  • Combinatorial formulas
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