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Extremal Projectors of q-Boson Algebras

Toshiki Nakashima
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Abstract

We define the extremal projector of the $q$-boson Kashiwara algebra $B_q(\ge)$ and study their basic properties. Applying their proerties to the representation theory of the category ${\cal O}(B_q(\ge))$, whose objects are ''upper bounded '' $B_q(\ge)$-modules, we obtain its semi-simplicity and the classification of simple modules.

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Toshiki Nakashima. 2002-06-24. Extremal Projectors of q-Boson Algebras. https://arxiv.org/abs/math/0206243

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