We give two constructions for each fundamental representation of sp 2 n, β«ήβ¬ . We also present quantum versions of these constructions. These are explicit in the sense of the GelfandαTsetlin constructions of the irreducible representations of Ε½ . Ε½ . gl n, β«ήβ¬ : we explicitly specify the matrix elem
A Basis for Representations of Symplectic Lie Algebras
β Scribed by A. I. Molev
- Publisher
- Springer
- Year
- 1999
- Tongue
- English
- Weight
- 213 KB
- Volume
- 201
- Category
- Article
- ISSN
- 0010-3616
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π SIMILAR VOLUMES
In this work a large number of irreducible representations with finite dimensional weight spaces are constructed for some toroidal Lie algebras. To accomplish this we develop a general theory of β«ήβ¬ n -graded Lie algebras with polynomial multiplication. We construct modules by the standard inducing
Leibniz representation of the Lie algebra α is a vector space M equipped with Ε½ .w x w x two actions left and right α, α : α m M Βͺ M and α, α : M m α Βͺ M which satisfy the relations \* Partially supported by Grant INTAS-93-2618. 414
Let F be an algebraically closed field of characteristic = 2, 3, W a F -vector space and The faithful irreducible L-modules are determined. It is shown that L has minimal ideals. If a minimal ideal S is infinite-dimensional then SW is a completely reducible L-module. Suppose L β© fgl(W ) = (0), W is