Exponential Tensor Modules
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Date
2022-06-02Author
Nguyen, Khoa Hoang
0000-0001-7556-5346
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Representation theory of Lie algebra of a finite dimensional reductive Lie algebra g is a long-standing problem. The ultimate goal is to classify all representations of g. However. the only case only case when a complete classification is obtained is the case of g = sl(2). Hence, it is natural to study certain categories of representations of g for which some finiteness conditions on the action of certain elements of g is enforced. In this thesis, we introduce a class of representations T (g, V, S) of sl(n + 1) of mixed tensor type. By varying the polynomial g, the gl(n)-module V , and the set S, we obtain important classes of weight representations over the Cartan subalgebra h of sl(n + 1), and representations that are free over h. Moreover, An isomorphism theorem and simplicity criterion for T(g,V,S) is provided.