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Induced Modules for Affine Lie Algebras
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2009, том 5
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Induced Modules for Affine Lie Algebras
Інший ID:
2000 Mathematics Subject Classification: 17B65; 17B67
Посилання:
Induced Modules for Affine Lie Algebras / V. Futorny, I. Kashuba // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 22 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Kac–Moody Algebras and Applications. The first author is supported in part by the CNPq grant (301743/2007-0) and by the Fapesp grant (2005/60337-2). The second author is supported by the Fapesp grant (2007/025861).
Дата:
2009
Переглядів:
459
Завантажень:
252
Анотація:
We study induced modules of nonzero central charge with arbitrary multiplicities over affine Lie algebras. For a given pseudo parabolic subalgebra P of an affine Lie algebra G, our main result establishes the equivalence between a certain category of P-induced G-modules and the category of weight P-modules with injective action of the central element of G. In particular, the induction functor preserves irreducible modules. If P is a parabolic subalgebra with a finite-dimensional Levi factor then it defines a unique pseudo parabolic subalgebra Pps, P Ì Pps. The structure of P-induced modules in this case is fully determined by the structure of Pps-induced modules. These results generalize similar reductions in particular cases previously considered by V. Futorny, S. König, V. Mazorchuk [Forum Math. 13 (2001), 641-661], B. Cox [Pacific J. Math. 165 (1994), 269-294] and I. Dimitrov, V. Futorny, I. Penkov [Comm. Math. Phys. 250 (2004), 47-63].
