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 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

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.

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 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
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