The aim of this seminar is to introduce the theory of Schur functors, with an aim of being able to compute these in specific applications. Let $K$ be a commutative ring. We recall that the $n$-th tensor power $E^{\otimes n}$ of a module $E$ represents the functor sending a module $M$ to the set (in fact $K$-module) of multilinear maps $E^n o M$. Similarly we can define the $n$-th exterior power $\bigwedge^n(E)$ as the module representing the functor of alternating multilinear maps, and the $n$-th symmetric power $\mathrm{Sym}^n(E)$ as representing the functor of symmetric multilinear maps. The Schur functors generalise these concepts: for each partition $\lambda$ one obtains a module $S^\lambda(E)$ representing a certain class of multilinear maps such that $S^{(1^n)}(E)\cong\bigwedge^n(E)$
| Identifier (URI) | Rank |
|---|---|
| dbkwik:resource/6zwbRl7nGbj2RvNGPrW-AA== | 5.88129e-14 |