Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.06333 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916281793380352 |
|---|---|
| author | Baine, J. |
| author_facet | Baine, J. |
| contents | By studying a categorification of the antisymmetriser quasi-idempotent in the Hecke algebra, we derive a closed formula for the Jones-Wenzl idempotent in the Temperley-Lieb algebra. In particular, we show that when the idempotent is expressed in terms of the monomial basis, the coefficients are the graded ranks of certain indecomposable Soergel modules. Equivalently, the coefficients can be expressed as a ratio of certain Kazhdan-Lusztig polynomials. Similar results are obtained for generalised Jones-Wenzl idempotents in other types. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_06333 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the coefficients in the Jones-Wenzl idempotent Baine, J. Representation Theory By studying a categorification of the antisymmetriser quasi-idempotent in the Hecke algebra, we derive a closed formula for the Jones-Wenzl idempotent in the Temperley-Lieb algebra. In particular, we show that when the idempotent is expressed in terms of the monomial basis, the coefficients are the graded ranks of certain indecomposable Soergel modules. Equivalently, the coefficients can be expressed as a ratio of certain Kazhdan-Lusztig polynomials. Similar results are obtained for generalised Jones-Wenzl idempotents in other types. |
| title | On the coefficients in the Jones-Wenzl idempotent |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2406.06333 |