A Spin Analogue of Kerov Polynomials
Kerov polynomials describe normalized irreducible characters of the symmetric groups in terms of the free cumulants associated with Young diagrams. We suggest well-suited counterparts of the Kerov polynomials in spin (or projective) representation settings. We show that spin analogues of irreducible...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2018 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2018
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209519 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | A Spin Analogue of Kerov Polynomials / S. Matsumoto // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 22 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862656482522169344 |
|---|---|
| author | Matsumoto, S. |
| author_facet | Matsumoto, S. |
| citation_txt | A Spin Analogue of Kerov Polynomials / S. Matsumoto // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 22 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Kerov polynomials describe normalized irreducible characters of the symmetric groups in terms of the free cumulants associated with Young diagrams. We suggest well-suited counterparts of the Kerov polynomials in spin (or projective) representation settings. We show that spin analogues of irreducible characters are polynomials in even free cumulants associated with double diagrams of strict partitions. Moreover, we present a conjecture for the positivity of their coefficients.
|
| first_indexed | 2025-12-07T14:52:10Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209519 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T14:52:10Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Matsumoto, S. 2025-11-24T10:25:41Z 2018 A Spin Analogue of Kerov Polynomials / S. Matsumoto // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 22 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 05E10; 20C30; 05E05 arXiv: 1803.01121 https://nasplib.isofts.kiev.ua/handle/123456789/209519 https://doi.org/10.3842/SIGMA.2018.053 Kerov polynomials describe normalized irreducible characters of the symmetric groups in terms of the free cumulants associated with Young diagrams. We suggest well-suited counterparts of the Kerov polynomials in spin (or projective) representation settings. We show that spin analogues of irreducible characters are polynomials in even free cumulants associated with double diagrams of strict partitions. Moreover, we present a conjecture for the positivity of their coefficients. The author acknowledges useful discussions with Valentin Féray and Dario De Stavola. The research was supported by JSPS KAKENHI Grant Number 17K05281. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Spin Analogue of Kerov Polynomials Article published earlier |
| spellingShingle | A Spin Analogue of Kerov Polynomials Matsumoto, S. |
| title | A Spin Analogue of Kerov Polynomials |
| title_full | A Spin Analogue of Kerov Polynomials |
| title_fullStr | A Spin Analogue of Kerov Polynomials |
| title_full_unstemmed | A Spin Analogue of Kerov Polynomials |
| title_short | A Spin Analogue of Kerov Polynomials |
| title_sort | spin analogue of kerov polynomials |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209519 |
| work_keys_str_mv | AT matsumotos aspinanalogueofkerovpolynomials AT matsumotos spinanalogueofkerovpolynomials |