Symmetry, Integrability and Geometry: Methods and Applications
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



SIGMA:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Symmetry, Integrability and Geometry: Methods and Applications, 2018, Volume 14, 038, 21 pp.
DOI: https://doi.org/10.3842/SIGMA.2018.038
(Mi sigma1337)
 

This article is cited in 1 scientific paper (total in 1 paper)

Homomorphisms from Specht Modules to Signed Young Permutation Modules

Kay Jin Lima, Kai Meng Tanb

a Division of Mathematical Sciences, Nanyang Technological University, SPMS-PAP-03-01, 21 Nanyang Link, 637371 Singapore
b Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, 119076 Singapore
Full-text PDF (476 kB) Citations (1)
References:
Abstract: We construct a class $\Theta_{\mathscr{R}}$ of homomorphisms from a Specht module $S_{\mathbb{Z}}^{\lambda}$ to a signed permutation module $M_{\mathbb{Z}}(\alpha|\beta)$ which generalises James's construction of homomorphisms whose codomain is a Young permutation module. We show that any $\phi \in \mathrm{Hom}_{{\mathbb{Z}}\mathfrak{S}_n}\big(S_{\mathbb{Z}}^\lambda, M_{\mathbb{Z}}(\alpha|\beta)\big)$ lies in the $\mathbb{Q}$-span of $\Theta_{\text{sstd}}$, a subset of $\Theta_{\mathbb{R}}$ corresponding to semistandard $\lambda$-tableaux of type $(\alpha|\beta)$. We also study the conditions for which $\Theta^{\mathbb{Z}}_{\mathrm{sstd}}$ – a subset of $\mathrm{Hom}_{{\mathbb{Z}}\mathfrak{S}_n}\big(S_{\mathbb{Z}}^\lambda,M_{\mathbb{Z}}(\alpha|\beta)\big)$ induced by $\Theta_{\mathrm{sstd}}$ – is linearly independent, and show that it is a basis for $\mathrm{Hom}_{{\mathbb{Z}}\mathfrak{S}_n}\big(S_{\mathbb{Z}}^\lambda,M_{\mathbb{Z}}(\alpha|\beta)\big)$ when ${\mathbb{Z}}\mathfrak{S}_n$ is semisimple.
Keywords: symmetric group; Specht module; signed Young permutation module; homomorphism.
Funding agency Grant number
Ministry of Education, Singapore Tier 2 AcRF MOE2015-T2-2-003
Supported by Singapore MOE Tier 2 AcRF MOE2015-T2-2-003.
Received: July 14, 2017; in final form April 18, 2018; Published online April 25, 2018
Bibliographic databases:
Document Type: Article
MSC: 20C30
Language: English
Citation: Kay Jin Lim, Kai Meng Tan, “Homomorphisms from Specht Modules to Signed Young Permutation Modules”, SIGMA, 14 (2018), 038, 21 pp.
Citation in format AMSBIB
\Bibitem{LimTan18}
\by Kay~Jin~Lim, Kai~Meng~Tan
\paper Homomorphisms from Specht Modules to Signed Young Permutation Modules
\jour SIGMA
\yr 2018
\vol 14
\papernumber 038
\totalpages 21
\mathnet{http://mi.mathnet.ru/sigma1337}
\crossref{https://doi.org/10.3842/SIGMA.2018.038}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000431680000001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85046542489}
Linking options:
  • https://www.mathnet.ru/eng/sigma1337
  • https://www.mathnet.ru/eng/sigma/v14/p38
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
    Statistics & downloads:
    Abstract page:305
    Full-text PDF :31
    References:21
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024