A combinatorial model for the transition matrix between the Specht and $\operatorname {SL}_2$ -web bases
We introduce a new class of permutations, called web permutations. Using these permutations, we provide a combinatorial interpretation for entries of the transition matrix between the Specht and $\operatorname {SL}_2$ -web bases of the irreducible $ \mathfrak {S}_{2n} $ -representation i...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2023-01-01
|
| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509423000798/type/journal_article |
| _version_ | 1797680490479616000 |
|---|---|
| author | Byung-Hak Hwang Jihyeug Jang Jaeseong Oh |
| author_facet | Byung-Hak Hwang Jihyeug Jang Jaeseong Oh |
| author_sort | Byung-Hak Hwang |
| collection | DOAJ |
| description | We introduce a new class of permutations, called web permutations. Using these permutations, we provide a combinatorial interpretation for entries of the transition matrix between the Specht and
$\operatorname {SL}_2$
-web bases of the irreducible
$ \mathfrak {S}_{2n} $
-representation indexed by
$ (n,n) $
, which answers Rhoades’s question. Furthermore, we study enumerative properties of these permutations. |
| first_indexed | 2024-03-11T23:30:47Z |
| format | Article |
| id | doaj.art-5f8569eab10d4021b48c208f665c58f1 |
| institution | Directory Open Access Journal |
| issn | 2050-5094 |
| language | English |
| last_indexed | 2024-03-11T23:30:47Z |
| publishDate | 2023-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj.art-5f8569eab10d4021b48c208f665c58f12023-09-20T09:14:55ZengCambridge University PressForum of Mathematics, Sigma2050-50942023-01-011110.1017/fms.2023.79A combinatorial model for the transition matrix between the Specht and $\operatorname {SL}_2$ -web basesByung-Hak Hwang0Jihyeug Jang1Jaeseong Oh2https://orcid.org/0000-0002-6110-2188Anyang, South Korea; E-mail:Department of Mathematics, Sungkyunkwan University (SKKU), Suwon, Gyeonggi-do 16419, South Korea; E-mail:Yonsei Mathematical Sciences and Computation, Yonsei University, 50 Yonsei-Ro, Seodaemun-Gu, Seoul 03722, South Korea; E-mail:We introduce a new class of permutations, called web permutations. Using these permutations, we provide a combinatorial interpretation for entries of the transition matrix between the Specht and $\operatorname {SL}_2$ -web bases of the irreducible $ \mathfrak {S}_{2n} $ -representation indexed by $ (n,n) $ , which answers Rhoades’s question. Furthermore, we study enumerative properties of these permutations.https://www.cambridge.org/core/product/identifier/S2050509423000798/type/journal_article05E1005A1520C30 |
| spellingShingle | Byung-Hak Hwang Jihyeug Jang Jaeseong Oh A combinatorial model for the transition matrix between the Specht and $\operatorname {SL}_2$ -web bases Forum of Mathematics, Sigma 05E10 05A15 20C30 |
| title | A combinatorial model for the transition matrix between the Specht and $\operatorname {SL}_2$ -web bases |
| title_full | A combinatorial model for the transition matrix between the Specht and $\operatorname {SL}_2$ -web bases |
| title_fullStr | A combinatorial model for the transition matrix between the Specht and $\operatorname {SL}_2$ -web bases |
| title_full_unstemmed | A combinatorial model for the transition matrix between the Specht and $\operatorname {SL}_2$ -web bases |
| title_short | A combinatorial model for the transition matrix between the Specht and $\operatorname {SL}_2$ -web bases |
| title_sort | combinatorial model for the transition matrix between the specht and operatorname sl 2 web bases |
| topic | 05E10 05A15 20C30 |
| url | https://www.cambridge.org/core/product/identifier/S2050509423000798/type/journal_article |
| work_keys_str_mv | AT byunghakhwang acombinatorialmodelforthetransitionmatrixbetweenthespechtandoperatornamesl2webbases AT jihyeugjang acombinatorialmodelforthetransitionmatrixbetweenthespechtandoperatornamesl2webbases AT jaeseongoh acombinatorialmodelforthetransitionmatrixbetweenthespechtandoperatornamesl2webbases AT byunghakhwang combinatorialmodelforthetransitionmatrixbetweenthespechtandoperatornamesl2webbases AT jihyeugjang combinatorialmodelforthetransitionmatrixbetweenthespechtandoperatornamesl2webbases AT jaeseongoh combinatorialmodelforthetransitionmatrixbetweenthespechtandoperatornamesl2webbases |