Character and dimension formulae for general linear superalgebra
| dc.creator | Su, Yucai | |
| dc.creator | Zhang, R. B. | |
| dc.date | 2004-03-19 | |
| dc.date | 2004-05-18 | |
| dc.date.accessioned | 2026-07-07T05:06:32Z | |
| dc.date.available | 2026-07-07T05:06:32Z | |
| dc.description | The generalized Kazhdan-Lusztig polynomials for the finite dimensional irreducible representations of the general linear superalgebra are computed explicitly. Using the result we establish a one to one correspondence between the set of composition factors of an arbitrary $r$-fold atypical $gl_{m|n}$-Kac-module and the set of composition factors of some $r$-fold atypical $gl_{r|r}$-Kac-module. The result of Kazhdan-Lusztig polynomials is also applied to prove a conjectural character formula put forward by van der Jeugt et al in the late 80s. We simplify this character formula to cast it into the Kac-Weyl form, and derive from it a closed formula for the dimension of any finite dimensional irreducible representation of the general linear superalgebra. | |
| dc.description | 28 pages, re-writing results in terms of height vectors and adding one more result | |
| dc.identifier | https://arxiv.org/abs/math/0403315 | |
| dc.identifier | http://arxiv.org/abs/math/0403315 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70509 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Representation Theory | |
| dc.subject | 17B10 | |
| dc.title | Character and dimension formulae for general linear superalgebra | |
| dc.type | text |