Homomorphisms from Specht Modules to Signed Young Permutation Modules
We construct a class ΘR of homomorphisms from a Specht module SλZ to a signed permutation module MZ(α|β), which generalises James's construction of homomorphisms whose codomain is a Young permutation module. We show that any ϕ ∈ HomZSn(SλZ, MZ(α|β)) lies in the Q-span of Θsstd, a subset of ΘR c...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2018 |
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| Sprache: | Englisch |
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Інститут математики НАН України
2018
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/209534 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Homomorphisms from Specht Modules to Signed Young Permutation Modules / K.J. Lim, K.M. Tan // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 14 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862546571740053504 |
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| author | Lim, K.J. Tan, K.M. |
| author_facet | Lim, K.J. Tan, K.M. |
| citation_txt | Homomorphisms from Specht Modules to Signed Young Permutation Modules / K.J. Lim, K.M. Tan // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 14 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We construct a class ΘR of homomorphisms from a Specht module SλZ to a signed permutation module MZ(α|β), which generalises James's construction of homomorphisms whose codomain is a Young permutation module. We show that any ϕ ∈ HomZSn(SλZ, MZ(α|β)) lies in the Q-span of Θsstd, a subset of ΘR corresponding to semistandard λ-tableaux of type (α|β). We also study the conditions for which ΘFsstd-a subset of HomFSn(SλF, MF(α|β)) induced by Θsstd-is linearly independent, and show that it is a basis for HomFSn(SλF, MF(α|β)) when FSn is semisimple.
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| first_indexed | 2025-12-03T18:36:32Z |
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| id | nasplib_isofts_kiev_ua-123456789-209534 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-03T18:36:32Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
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| spelling | Lim, K.J. Tan, K.M. 2025-11-24T10:45:06Z 2018 Homomorphisms from Specht Modules to Signed Young Permutation Modules / K.J. Lim, K.M. Tan // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 14 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 20C30 arXiv: 1606.00542 https://nasplib.isofts.kiev.ua/handle/123456789/209534 https://doi.org/10.3842/SIGMA.2018.038 We construct a class ΘR of homomorphisms from a Specht module SλZ to a signed permutation module MZ(α|β), which generalises James's construction of homomorphisms whose codomain is a Young permutation module. We show that any ϕ ∈ HomZSn(SλZ, MZ(α|β)) lies in the Q-span of Θsstd, a subset of ΘR corresponding to semistandard λ-tableaux of type (α|β). We also study the conditions for which ΘFsstd-a subset of HomFSn(SλF, MF(α|β)) induced by Θsstd-is linearly independent, and show that it is a basis for HomFSn(SλF, MF(α|β)) when FSn is semisimple. Supported by Singapore MOE Tier 2 AcRF MOE2015-T2-2-003. We thank the guest editors for bringing to our attention the work of Du and Rui on signed q-permutation modules of the Iwahori–Hecke algebras of type A [4], and the referees for their helpful comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Homomorphisms from Specht Modules to Signed Young Permutation Modules Article published earlier |
| spellingShingle | Homomorphisms from Specht Modules to Signed Young Permutation Modules Lim, K.J. Tan, K.M. |
| title | Homomorphisms from Specht Modules to Signed Young Permutation Modules |
| title_full | Homomorphisms from Specht Modules to Signed Young Permutation Modules |
| title_fullStr | Homomorphisms from Specht Modules to Signed Young Permutation Modules |
| title_full_unstemmed | Homomorphisms from Specht Modules to Signed Young Permutation Modules |
| title_short | Homomorphisms from Specht Modules to Signed Young Permutation Modules |
| title_sort | homomorphisms from specht modules to signed young permutation modules |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209534 |
| work_keys_str_mv | AT limkj homomorphismsfromspechtmodulestosignedyoungpermutationmodules AT tankm homomorphismsfromspechtmodulestosignedyoungpermutationmodules |