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arxiv: math/0206243 · v1 · submitted 2002-06-24 · 🧮 math.QA · math.RT

Extremal Projectors of q-Boson Algebras

classification 🧮 math.QA math.RT
keywords extremalmodulesalgebraalgebrasapplyingbasicbosonbounded
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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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