scholarly journals New irreducible modules for Heisenberg and affine Lie algebras

2013 ◽  
Vol 373 ◽  
pp. 284-298 ◽  
Author(s):  
Viktor Bekkert ◽  
Georgia Benkart ◽  
Vyacheslav Futorny ◽  
Iryna Kashuba
Keyword(s):  
Lie Algebras ◽  
Affine Lie Algebras ◽  
Irreducible Modules

scholarly journals Irreducible modules for extended affine Lie algebras

2011 ◽  
Vol 327 (1) ◽  
pp. 208-235 ◽  
Author(s):  
Yuly Billig ◽  
Michael Lau
Keyword(s):  
Lie Algebras ◽  
Affine Lie Algebras ◽  
Irreducible Modules

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 A RECURRENCE RELATION FOR CHARACTERS OF HIGHEST WEIGHT INTEGRABLE MODULES FOR AFFINE LIE ALGEBRAS

2007 ◽  
Vol 09 (02) ◽  
pp. 121-133 ◽  
Author(s):  
WILLIAM J. COOK ◽  
HAISHENG LI ◽  
KAILASH C. MISRA
Keyword(s):  
Recurrence Relation ◽  
Lie Algebras ◽  
Vertex Operator ◽  
Recurrence Relations ◽  
Operator Algebras ◽  
Affine Lie Algebras ◽  
Highest Weight ◽  
Irreducible Modules ◽  
Level 1 ◽  
Integrable Modules

Using certain results for the vertex operator algebras associated with affine Lie algebras, we obtain recurrence relations for the characters of integrable highest weight irreducible modules for an affine Lie algebra. As an application we show that in the simply-laced level 1 case, these recurrence relations give the known characters, whose principal specializations naturally give rise to some multisum Macdonald identities.

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
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