Abstract
We prove the Kac–Wakimoto character formula for the general linear Lie superalgebra gl(m|n), which was conjectured by Kac and Wakimoto in 1994. This formula specializes to the well-known Kac–Weyl character formula when the modules are typical and to the Weyl denominator identity when the module is trivial. We also prove a determinantal character formula for KW-modules. In our proof, we demonstrate how to use odd reflections to move character formulas between the different sets of simple roots of a Lie superalgebra. As a consequence, we show that KW-modules are precisely Kostant modules, which were studied by Brundan and Stroppel, thus yielding a simple combinatorial defining condition for KW-modules and a classification of these modules.
Original language | English (US) |
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Pages (from-to) | 1419-1452 |
Number of pages | 34 |
Journal | Algebra and Number Theory |
Volume | 9 |
Issue number | 6 |
DOIs | |
State | Published - Sep 22 2015 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:©2015 Mathematical Sciences Publishers.
Keywords
- Character formulas
- Kazhdan–Lusztig polynomials
- Lie superalgebras
- Tame modules