Singular vectors corresponding to imaginary roots in verma modules over affine Lie algebras.
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Smallness problem for quantum affine algebras and quiver varieties
David Hernandez (2008)
Annales scientifiques de l'École Normale Supérieure
The geometric small property (Borho-MacPherson [2]) of projective morphisms implies a description of their singularities in terms of intersection homology. In this paper we solve the smallness problem raised by Nakajima [37, 35] for certain resolutions of quiver varieties [37] (analogs of the Springer resolution): for Kirillov-Reshetikhin modules of simply-laced quantum affine algebras, we characterize explicitly the Drinfeld polynomials corresponding to the small resolutions. We use an elimination...
Spacelike singularities and hidden symmetries of gravity.
Henneaux, Marc, Spindel, Philippe, Persson, Daniel (2008)
Living Reviews in Relativity [electronic only]
String functions for affine Lie algebras integrable modules.
Kulish, Petr, Lyakhovsky, Vladimir (2008)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Sugawara operators and Kac-Kazhdan conjecture.
Takahiro Hayashi (1988)
Inventiones mathematicae
Symmetries of the Kac-Peterson modular matrices of affine algebras.
Terry Gannon (1995)
Inventiones mathematicae
Symplectic K2 of Laurent polynomials, associated Kac-Moody groups and Witt rings.
Ulf Rehmann, Jun Morita (1991)
Mathematische Zeitschrift
Systèmes de racines infinis
Nicole Bardy (1996)
Mémoires de la Société Mathématique de France
Systèmes hamiltoniens complètement intégrables et déformations d'algèbres de Lie.
Faouzi Ammar (1994)
Publicacions Matemàtiques
Some of the completely integrable Hamiltonian systems obtained through Adler-Kostant-Symes theorem rely on two distinct Lie algebra structures on the same underlying vector space. We study here the cases when two structures are linked together by deformations.
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