Periodic modules and quantum groups
classification
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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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