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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2018 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209534 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| Summary: | 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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| ISSN: | 1815-0659 |