Representations of cyclotomic oriented Brauer categories

2021/02/13 by Gao, Mengmeng, Rui, Hebing, Song, Linliang
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2102.06918

Abstract

Let A be the locally unital algebra associated to a cyclotomic oriented Brauer category over an arbitrary algebraically closed field \Bbbk of characteristic p≥ 0. The category of locally finite dimensional representations of A is used to give the tensor product categorification (in the general sense of Losev and Webster) for an integrable lowest weight with an integrable highest weight representation of the same level for the Lie algebra \mathfrak g, where \mathfrak g is a direct sum of copies of \mathfrak sl_∞ (resp., \mathfrak sl_p ) if p=0 (resp., p>0). Such a result was expected in [3] when \Bbbk=\mathbb C and proved previously by Brundan in [2] when the level is 1.

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