Categorification of generic Su-Zhang character formula
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914304777781248 |
|---|---|
| author | Hirota, Shunsuke |
| author_facet | Hirota, Shunsuke |
| contents | For semisimple Lie algebras, the BGG resolution is often viewed as a categorification of the Weyl character formula. For general linear Lie superalgebras, Brundan--Stroppel constructed an infinite resolution of the so-called Kostant simple modules by Kac modules, but their construction does not directly generalize the classical BGG resolution.
In this paper we construct, for weights lying outside a neighborhood of the walls of the Weyl chambers, a resolution that categorifies a known Weyl-type finite-sum character formula in the same spirit as the Kac--Wakimoto formula. Our resolution is built from images of canonical homomorphisms between Verma modules attached to non-conjugate Borel subalgebras related by odd reflections. In particular, the construction developed here does generalize the classical BGG resolution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16095 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Categorification of generic Su-Zhang character formula Hirota, Shunsuke Representation Theory For semisimple Lie algebras, the BGG resolution is often viewed as a categorification of the Weyl character formula. For general linear Lie superalgebras, Brundan--Stroppel constructed an infinite resolution of the so-called Kostant simple modules by Kac modules, but their construction does not directly generalize the classical BGG resolution. In this paper we construct, for weights lying outside a neighborhood of the walls of the Weyl chambers, a resolution that categorifies a known Weyl-type finite-sum character formula in the same spirit as the Kac--Wakimoto formula. Our resolution is built from images of canonical homomorphisms between Verma modules attached to non-conjugate Borel subalgebras related by odd reflections. In particular, the construction developed here does generalize the classical BGG resolution. |
| title | Categorification of generic Su-Zhang character formula |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2512.16095 |