Characters of irreducible modules with non-critical highest weights over affine Lie algebras [PDF]
, 1999 Masaki Kashiwara, Toshiyuki Tanisaki
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Chevalley involutions for Lie tori and extended affine Lie algebras [PDF]
, 2023 Saeid Azam, Mehdi Farhadi Izadi
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Extended Affine Lie Algebras and their Vertex Representations
Publications of the Research Institute for Mathematical Sciences, 1989 \textit{K. Saito} has introduced the concept of extended affine root systems to construct a flat structure for the space of the universal deformation of a simple elliptic singularity [Publ. Res. Inst. Math. Sci. 21, 75--179 (1985; Zbl 0573.17012)]. It is by definition an extension of an affine root system by one dimensional radical.
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Affine and Finite Lie Algebras and Integrable Toda Field Equations on Discrete Space-Time
Symmetry, Integrability and Geometry: Methods and Applications, 2012 Difference-difference systems are suggested corresponding to the Cartan matrices of any simple or affine Lie algebra. In the cases of the algebras $A_N$, $B_N$, $C_N$, $G_2$, $D_3$, $A_1^{(1)}$, $A_2^{(2)}$, $D^{(2)}_N$ these systems are proved to be ...
Rustem Garifullin +2 more
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Basic Representations for Classical Affine Lie Algebras
Journal of Algebra, 2000 Presented here is a construction of certain bases of basic representations for classical affine Lie algebras. The starting point is a Z-grading g = g_{-1} + g_0 + g_1 of a classical Lie algebra g and the corresponding decomposition tilde g = tilde g_{-1} + tilde g_0 + tilde g_1 of the affine Lie algebra tilde g. By using a generalization of Frenkel-Kac
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Horizontally Affine Functions on Step-2 Carnot Algebras. [PDF]
J Geom Anal, 2023 Le Donne E, Morbidelli D, Rigot S.
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A differential graded Lie algebra controlling the Poisson deformations\n of an affine Poisson variety [PDF]
, 2018 Matej Filip
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Weyl-Kac character formula for affine Lie algebras in Deligne's categories [PDF]
, 2021 Aleksei Pakharev
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The PBW Filtration, Demazure Modules and Toroidal Current Algebras
Symmetry, Integrability and Geometry: Methods and Applications, 2008 Let L be the basic (level one vacuum) representation of the affine Kac-Moody Lie algebra ^g. The m-th space F_m of the PBW filtration on L is a linear span of vectors of the form x_1dots x_lv_0, where l ≤ m, x_i in ^g and v_0 is a highest weight vector ...
Evgeny Feigin
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Integrable representations for toroidal extended affine Lie algebras [PDF]
, 2017 Fulin Chen, Zhiqiang Li, Shaobin Tan
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