TITLE: Decomposition of $\bigotimes^{m} \mathbb{C}^{n}$ under the action of $\operatorname{GL}_{n}\times \operatorname{S}_{m}$
QUESTION [7 upvotes]: $\DeclareMathOperator\GL{GL}\DeclareMathOperator\S{S}$I want to know the proof of the following theorem. It is stated somewhere that, a proof can be found in: "Roger Howe, Perspectives on invariant theory: Schur duality, multiplicity-free actions and
beyond, The Schur lectures (1992) (Tel Aviv), Israel Math. Conf. Proc., vol. 8, Bar-Ilan Univ.,
Ramat Gan, 1995, pp. 1–182, DOI 10.1007/BF02771542. MR1321638 (96e:13006)".
However, I am not able to access this. Could anyone help me out to find this paper, or may be, is there any other place where I can find the proof?
Theorem: Let $F^{\lambda}_{n}$ denote the irreducible rational representation
of $\operatorname{GL}_{n}$ with highest weight indexed by $\lambda$. Let $W^{\lambda}_{m}$ denote the irreducible complex representation of $\S_{m}$ indexed by $\lambda$. Under the joint action of $\GL_{n}\times \S_{m}$ on $\bigotimes^{m} \mathbb{C}^{n}$, we have the multiplicity free decomposition $$ \bigotimes^{m} \mathbb{C}^{n} \cong \bigoplus_{\lambda} F^{\lambda}_{n} \otimes W^{\lambda}_{m} $$
where the sum is over all partitions $\lambda$ of $m$ with at most $n$ parts. Note that all
irreducible representations of $\S_{m}$ appear in the decomposition when $n \geq m$.

REPLY [4 votes]: A good reference for the Schur-Weyl duality (and also for generalization of this to other classical groups) I can recommend Symmetry, Representations, and Invariants by Roe  Goodman and Nolan Wallach.