A character formula for atypical critical gl(m/n) representations labelled by composite partitions

作者：Moens EM^*; Van der Jeugt J

来源：Journal of Physics A: Mathematical and General , 2004, 37(50): 12019-12039.

DOI：10.1088/0305-4470/37/50/006

Let g be the Lie superalgebra gl(m\n). We show how to associate a gl(m\n) weight A to a composite partition V; it with composite Young diagram F((nu) over bar; mu). Based upon the definition of critical representations, the notion of 'critical composite partition' is introduced. It is shown that for critical composite partitions (subject to a technical restriction) the corresponding gl(m\n) representation V-Lambda is tame, so its character formula can be computed. This character is shown to coincide with the composite S-function S-(nu) over bar;mu (x/y).

• 出版日期2004-12-17