Hecke-Clifford superalgebras and crystals of type D⁽²⁾_l

2009/07/28 by Tsuchioka, Shunsuke
#05E10 #20C08 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.0907.4936

Abstract

Brundan and Kleshchev showed that some parts of the representation theory of the affine Hecke-Clifford superalgebras and its finite-dimensional "cyclotomic" quotients are controlled by the Lie theory of type A⁽²⁾_2l when the quantum parameter q is a primitive (2l+1)-th root of unity. We show in this paper that similar theorems hold when q is a primitive 4l-th root of unity by replacing the Lie theory of type A⁽²⁾_2l with that of type D⁽²⁾_l.

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