Structure of certain Verma modules over affine Lie algebras

1991 ◽  
Vol 24 (4) ◽  
pp. 332-334
Author(s):  
F. G. Malikov
Keyword(s):  
Lie Algebras ◽  
Verma Modules ◽  
Affine Lie Algebras

Imaginary Verma Modules for Affine Lie Algebras

1994 ◽  
Vol 37 (2) ◽  
pp. 213-218 ◽  
Author(s):  
V. M. Futorny
Keyword(s):  
Lie Algebras ◽  
Borel Subalgebra ◽  
Verma Modules ◽  
Affine Lie Algebras ◽  
Infinite Dimensions ◽  
Irreducible Modules

AbstractWe study a class of irreducible modules for Affine Lie algebras which possess weight spaces of both finite and infinite dimensions. These modules appear as the quotients of "imaginary Verma modules" induced from the "imaginary Borel subalgebra".

scholarly journals Equivalence of certain categories of modules for quantized affine lie algebras

2000 ◽  
Vol 69 (2) ◽  
pp. 162-175
Author(s):  
Vyacheslav M. Futorny ◽  
Duncan J. Melville
Keyword(s):  
Quantum Group ◽  
Lie Algebras ◽  
Verma Module ◽  
Verma Modules ◽  
Affine Lie Algebras ◽  
Finite Part ◽  
Moody Algebra ◽  
Finite Dimensional ◽  
Equivalence Of Categories ◽  
Category Of Modules

AbstractWe show that a quantum Verma-type module for a quantum group associated to an affine Kac-Moody algebra is characterized by its subspace of finite-dimensional weight spaces. In order to do this we prove an explicit equivalence of categories between a certain category containing the quantum Verma modules and a category of modules for a subalgebra of the quantum group for which the finite part of the Verma module is itself a module.

A class of non-standard modules for affine Lie algebras

1987 ◽  
Vol 196 (3) ◽  
pp. 303-313 ◽  
Author(s):  
Nolan R. Wallach
Keyword(s):  
Lie Algebras ◽  
Affine Lie Algebras

QUANTUM HAMILTONIAN REDUCTION AND WB ALGEBRA

1992 ◽  
Vol 07 (20) ◽  
pp. 4885-4898 ◽  
Author(s):  
KATSUSHI ITO
Keyword(s):  
Lie Algebras ◽  
Free Field ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Hamiltonian Reduction ◽  
Affine Lie Algebras ◽  
Quantum Hamiltonian Reduction ◽  
Free Field Realization ◽  
Coset Construction ◽  
Quantum Hamiltonian

We study the quantum Hamiltonian reduction of affine Lie algebras and the free field realization of the associated W algebra. For the nonsimply laced case this reduction does not agree with the usual coset construction of the W minimal model. In particular, we find that the coset model [Formula: see text] can be obtained through the quantum Hamiltonian reduction of the affine Lie superalgebra B(0, n)(1). To show this we also construct the Feigin-Fuchs representation of affine Lie superalgebras.

scholarly journals Braided Tensor Categories of Admissible Modules for Affine Lie Algebras

2018 ◽  
Vol 362 (3) ◽  
pp. 827-854 ◽  
Author(s):  
Thomas Creutzig ◽  
Yi-Zhi Huang ◽  
Jinwei Yang
Keyword(s):  
Lie Algebras ◽  
Affine Lie Algebras ◽  
Tensor Categories
Sign in / Sign up

Export Citation Format

Share Document