The problem of deciding the positivity of Kronecker coefficients and Saxl conjecture
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912729251446784 |
|---|---|
| author | Ebrahimi, Mahdi |
| author_facet | Ebrahimi, Mahdi |
| contents | Given an positive integer $k$, let $n:=\binom{k+1}{2}$. In 2012, during a talk at UCLA, Jan Saxl conjectured that all irreducible representations of the symmetric group $S_n$ occur in the decomposition of the tensor square of the irreducible representation corresponding to the staircase partition. In this paper, we investigate two useful methods to obtain some irreducible representations that occur in this decomposition. Our main tolls are the semi-group property for Kronecker coefficients and generalized blocks of symmetric groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03484 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The problem of deciding the positivity of Kronecker coefficients and Saxl conjecture Ebrahimi, Mahdi Representation Theory Combinatorics 05E10, 20C30, 05A17 Given an positive integer $k$, let $n:=\binom{k+1}{2}$. In 2012, during a talk at UCLA, Jan Saxl conjectured that all irreducible representations of the symmetric group $S_n$ occur in the decomposition of the tensor square of the irreducible representation corresponding to the staircase partition. In this paper, we investigate two useful methods to obtain some irreducible representations that occur in this decomposition. Our main tolls are the semi-group property for Kronecker coefficients and generalized blocks of symmetric groups. |
| title | The problem of deciding the positivity of Kronecker coefficients and Saxl conjecture |
| topic | Representation Theory Combinatorics 05E10, 20C30, 05A17 |
| url | https://arxiv.org/abs/2511.03484 |