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arxiv: math/0211437 · v3 · submitted 2002-11-27 · 🧮 math.RT

Periodic modules and quantum groups

classification 🧮 math.RT
keywords moduleperiodicelementsproveactuallybasiscanonicalcase
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We prove that the elements $A_\leq$ defined by Lusztig in a completion of the periodic module actually live in the periodic module, in the type A case. In order to prove this, we compare, using Schur duality, these elements with the Kashiwara canonical basis of an integrable module.

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