no. 3
The structure of the tensor product of 𝔽 2 [-] with a finite functor between 𝔽 2 -vector spaces
Annales de l'Institut Fourier, Tome 50 (2000) no. 3, pp. 781-805

The paper studies the structure of functors I⊗F in the category of functors from finite dimensional 𝔽 2 -vector spaces to 𝔽 2 -vector spaces, where F is a finite functor and I is the injective functor V↦𝔽 2 V * . A detection theorem is proved for sub-functors of such functors, which is the basis of the proof that the functors I⊗F are artinian of type one.

Soit ℱ la catégorie de foncteurs de la catégorie des 𝔽 2 -espaces vectoriels de dimension finie dans la catégorie des 𝔽 2 -espaces vectoriels. Nous étudions la structure du foncteur I⊗F∈ℱ, où F est un foncteur fini et I désigne le foncteur injectif V↦𝔽 2 V * . Un théorème de détection de sous-foncteurs de I⊗F est démontré, ce qui est la base de la démonstration que le foncteur I⊗F est artinien de type un.

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     author = {Powell, Geoffrey M. L.},
     title = {The structure of the tensor product of ${\mathbb {F}}_2[-]$ with a finite functor between ${\mathbb {F}}_2$-vector spaces},
     journal = {Annales de l'Institut Fourier},
     pages = {781--805},
     year = {2000},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {50},
     number = {3},
     doi = {10.5802/aif.1773},
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     mrnumber = {2001h:20065},
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}
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Powell, Geoffrey M. L. The structure of the tensor product of ${\mathbb {F}}_2[-]$ with a finite functor between ${\mathbb {F}}_2$-vector spaces. Annales de l'Institut Fourier, Tome 50 (2000) no. 3, pp. 781-805. doi: 10.5802/aif.1773

[J] G.D. James, The representation theory of the symmetric groups, Lecture Notes in Math., 682 (1978). | Zbl | MR

[J2] G.D. James, The decomposition of tensors over finite fields of prime characteristic, Math. Zeit., 172 (1980), 161-178. | Zbl | MR | EuDML

[JK] G.D. James, A. Kerber, The Representation Theory of the Symmetric Groups, Ency. Math. Appl., Addison-Wesley, Vol. 16, 1981. | Zbl | MR

[K1] N.J. Kuhn, Generic representations of the finite general linear groups and the Steenrod algebra : I, Amer. J. Math., 116 (1993), 327-360. | Zbl | MR

[K2] N.J. Kuhn, Generic representations of the finite general linear groups and the Steenrod algebra : II, K-Theory, 8 (1994), 395-426. | Zbl | MR

[K3] N.J. Kuhn, Generic representations of the finite general linear groups and the Steenrod algebra : III, K-Theory, 9 (1995), 273-303. | Zbl | MR

[PS] L. Piriou, L. Schwartz, Extensions de foncteurs simples, K-theory, 15 (1998), 269-291. | Zbl | MR

[P1] G.M.L. Powell, with an Appendix by L. SCHWARTZ, The Artinian conjecture for I ⊗ I, J. Pure Appl. Alg., 128 (1998), 291-310. | Zbl

[P2] G.M.L. Powell, Polynomial filtrations and Lannes' T-functor, K-Theory, 13 (1998), 279-304. | Zbl | MR

[P3] G.M.L. Powell, The structure of Ī⊗Λn in generic representation theory, J. Alg., 194 (1997), 455-466. | Zbl | MR

[P4] G.M.L. Powell, The structure of the indecomposable injectives in generic representation theory, Trans. Amer. Math. Soc., 350 (1998), 4167-4193. | Zbl | MR

[P5] G.M.L. Powell, On artinian objects in the category of functors between ℙ2-vector spaces, to appear in Proceedings of Euroconference 'Infinite Length Modules', Bielefeld, 1998. | Zbl

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