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Tabloids and weighted sums of characters of certain modules of the symmetric groups

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Title: Tabloids and weighted sums of characters of certain modules of the symmetric groups
Authors: Numata, Yasuhide Browse this author
Issue Date: Feb-2008
Publisher: Academic Press
Journal Title: European Journal of Combinatorics
Volume: 29
Issue: 2
Start Page: 480
End Page: 492
Publisher DOI: 10.1016/j.ejc.2007.02.007
Abstract: We consider certain modules of the symmetric groups whose basis elements are called tabloids. Some of these modules are isomorphic to subspaces of the cohomology rings of subvarieties of flag varieties as modules of the symmetric groups. We give a combinatorial description for some weighted sums of their characters, i.e., we introduce combinatorial objects called (½; l)-tableaux and rewrite weighted sums of characters as the numbers of these combinatorial objects. We also consider the meaning of these combinatorial objects, i.e., we construct a correspondence between (½; l)-tableaux and tabloids whose images are eigenvectors of the action of an element of cycle type ½ in quotient modules.
Type: article (author version)
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 沼田 泰英

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