Semisimplifications and representations of the General Linear Supergroup

2025/01/09 by Heidersdorf, Thorsten, Weissauer, Rainer
#17B10 #17B20 #17B55 #18M05 #18M25 #20G05 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2501.05298

Abstract

We study the semisimplification of the full karoubian subcategory generated by the irreducible finite dimensional representations of the algebraic supergroup GL(m|n) over an algebraically closed field of characteristic zero. This semisimplification is equivalent to the representations of a pro-reductive group H_m|n. We show that there is a canonical decomposition H_m|n ≅ GL(m - n) × H_n|n, thereby reducing the determination of H_m|n to the equal rank case m = n which was treated in a previous paper.

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