Geodesic
Imaginary Verma Modules for Affine Lie Algebras
Canadian mathematical bulletin, Tome 37 (1994) no. 2, pp. 213-218

Voir la notice de l'article provenant de la source Cambridge University Press

We 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".
DOI : 10.4153/CMB-1994-031-9
Mots-clés : 17B67, 17B10 
Futorny, V. M. Imaginary Verma Modules for Affine Lie Algebras. Canadian mathematical bulletin, Tome 37 (1994) no. 2, pp. 213-218. doi: 10.4153/CMB-1994-031-9
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[1] 1. Jakobsen, H. P. and Kac, V. G., A new class of unitarizable highest weight representations of infinitedimensional Lie algebras, Lecture Notes in Physics, 226(1985), 1–20. Google Scholar

[2] 2. Jakobsen, H. P. and Kac, V. G., A new class of unitarizable highest weight representations of infinite-dimensional Lie algebras, II,J. Funct. Anal. 82(1989), 69–90. Google Scholar

[3] 3. Futorny, V. M., On imaginary Verma modules over the Affine Lie algebra , Oslo Univ. 9(1991 ), preprint. Google Scholar

[4] 4. Futorny, V. M., Modules of Verma type for Affine Lie algebras, Funktsional. Anal, i Prilozhen., to appear. Google Scholar

[5] 5. Futorny, V. M., Root systems, representations and geometries, Ac. Sci. Ukrain. Math. 8(1990), 30–39. Google Scholar

[6] 6. Futorny, V. M., The parabolic subsets of root systems and corresponding representations of Affine Lie algebras, Contemp. Math (2) 131(1992), 45–52. Google Scholar

[7] 7. Kac, V. G., Infinite Dimensional Lie Algebras, Cambridge University Press, third edition, 1990. Google Scholar

[8] 8. Spirin, S. A., ℤ2 -graded modules with one-dimensional components over the Lie algebra Funktsional. Anal, i Prilozhen. 21(1987), 84–85. Google Scholar

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