Journal of Lie Theory 27 (2017), No. 4, 1069--1088
Copyright Heldermann Verlag 2017
A Weyl-Type Character Formula for PDC Modules of gl(m|n)
Michael Chmutov
School of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church Street SE, Minneapolis, MN 55455, U.S.A.
mchmutov@umn.edu
Crystal Hoyt
Department of Mathematics, Weizmann Institute of Science, 234 Herzl Street, Rehovot 76100, Israel
crystal.hoyt@weizmann.ac.il
Shifra Reif
Department of Mathematics, Bar-Ilan University, Ramat Gan 52900, Israel
shifra.reif@biu.ac.il
In 1994, Kac and Wakimoto suggested a generalization of Bernstein and Leites' character formula for basic Lie superalgebras, and the natural question was raised: to which simple highest weight modules does it apply? In this paper, we prove a similar formula for a large class of finite-dimensional simple modules over the Lie superalgebra gl(m|n), which we call piecewise disconnected modules, or PDC. The class of PDC modules naturally includes totally connected modules and totally disconnected modules, the two families for which similar character formulas were proven by Su and Zhang as special cases of their general formula. This paper is part of our program for the pursuit of elegant character formulas for Lie superalgebras.
Keywords: Lie superalgebra, highest weight module, Kac-Wakimoto character formula, piecewise disconnected weight.
MSC: 17B10, 05E10
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