Large annihilator category O for sl(∞),o(∞),sp(∞)

Add time:09/04/2019    Source:sciencedirect.com

We construct a new analogue of the BGG category O for the infinite-dimensional Lie algebras g=sl(∞),o(∞),sp(∞). A main difference with the categories studied in [9] and [2] is that all objects of our category satisfy the large annihilator condition introduced in [5]. Despite the fact that the splitting Borel subalgebras b of g are not conjugate, one can eliminate the dependency on the choice of b and introduce a universal highest weight category OLA of g-modules, the letters LA coming from “large annihilator”. The subcategory of integrable objects in OLA is precisely the category Tg studied in [5]. We investigate the structure of OLA, and in particular compute the multiplicities of simple objects in standard objects and the multiplicities of standard objects in indecomposable injectives. We also complete the annihilators in U(g) of simple objects of OLA.

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