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

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概要

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• 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.

• Academic Pressの論文

著者

• 沼田 泰英

  東京大学大学院情報理工学系研究科

• 沼田 泰英

  東京大学情報理工学系研究科・jst Crest

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