Geodesic
A Weyl-Type Character Formula for PDC Modules of gl(m|n)
Michael Chmutov1 ; Crystal Hoyt2 ; Shifra Reif3
1School of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church Street SE, Minneapolis, MN 55455, U.S.A.
2Department of Mathematics, Weizmann Institute of Science, 234 Herzl Street, Rehovot 76100, Israel
3Department of Mathematics, Bar-Ilan University, Ramat Gan 52900, Israel
Journal of Lie Theory, Tome 27 (2017) no. 4, pp. 1069-1088

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 17B10, 05E10
Mots-clés : Lie superalgebra, highest weight module, Kac-Wakimoto character formula, piecewise disconnected weight

Michael Chmutov  1   ; Crystal Hoyt  2   ; Shifra Reif  3

1 School of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church Street SE, Minneapolis, MN 55455, U.S.A.
2 Department of Mathematics, Weizmann Institute of Science, 234 Herzl Street, Rehovot 76100, Israel
3 Department of Mathematics, Bar-Ilan University, Ramat Gan 52900, Israel 
Michael Chmutov; Crystal Hoyt; Shifra Reif. A Weyl-Type Character Formula for PDC Modules of gl(m|n). Journal of Lie Theory, Tome 27 (2017) no. 4, pp. 1069-1088. http://geodesic.mathdoc.fr/item/JOLT_2017_27_4_a9/
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