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- W1562001036 abstract "AbstractLet be the coinvariant algebra of the symmetric group . The al gebra hasa natural gradation. For a xed ( 1 ), let ( ; ) (0 1 ) be the directsum of all the homogeneous components of whose degrees are co ngruent tomodulo . In this article, we will show that for each there exis ts a subgroupof and a representation ( ; ) of such that each ( ; ) is induced by ( ; ). 1. IntroductionThroughout this article, we follow [5] for fundamental term inology on partitions,Young tableaux and symmetric functions.A partition of a positive integer is a weakly decreasing sequence = ( 12 ) of nonnegative integers with 1 + 2 + + = . We also denote the parti-tion by (1 1 2 2 ), where is the multiplicity of in for 1 . If isa partition of , we simply write . The Young diagram of a partition is a setof points= ( ) Z 2 1in which we regard the coordinates increase from left to righ t, and from top to bottom.Let [ ] denote the set of integers 1 2 . A standard tableau of shape isa bijection : [ ] with the condition that the assigned numbers strictly increasealong both the rows and the columns in . We illustrate the Youn g diagram anda standard tableau for = (3 2 2) 7 in the following:= ,1 3 4= 2 56 7We denote by STab( ) the set of all the standard tableaux of sha pe .For a standard tableau of shape , dene the descent set Des( ) byDes( ) := [ 1] +1 is located in a lower row than in" @default.
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- W1562001036 date "2005-03-01" @default.
- W1562001036 modified "2023-09-26" @default.
- W1562001036 title "THE COINVARIANT ALGEBRA OF THE SYMMETRIC GROUP AS A DIRECT SUM OF INDUCED MODULES" @default.
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- W1562001036 doi "https://doi.org/10.18910/4880" @default.
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