GL n - DECOMPOSITION OF THE SCHUR COMPLEX S r (Λ 2 φ)

2003

In this paper we construct a natural filtration associated to the plethysm over arbitrary commutative ring R. Let : G longrightarrow F be a morphism of finite free R-modules. We construct the natural filtration of as a - complex such that its associated graded complex is , where is a set of partitions such that is a partition of which i-th term is . Specializing our result, we obtain the filtrations of $S_{r}(\wedge^2 F)\;and\;D_{r}(D_2G).㰌搀؀㘲㌮㠻Ⰰ䉵楬摩湧Ⱐ捯湳瑲畣瑩潮⁡湤⁣楶楬⁥湧楮敥物湧

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