# 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 (2000)

- Volume: 50, Issue: 3, page 781-805
- ISSN: 0373-0956

## Access Full Article

top## Abstract

top## How to cite

topPowell, 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 50.3 (2000): 781-805. <http://eudml.org/doc/75438>.

@article{Powell2000,

abstract = {The paper studies the structure of functors $I \otimes F$ in the category of functors from finite dimensional $\{\Bbb F\}_2$-vector spaces to $\{\Bbb F\}_2$-vector spaces, where $F$ is a finite functor and $I $ is the injective functor $V \mapsto \{\Bbb F\}_2^\{V^*\}$. A detection theorem is proved for sub-functors of such functors, which is the basis of the proof that the functors $I\otimes F$ are artinian of type one.},

author = {Powell, Geoffrey M. L.},

journal = {Annales de l'institut Fourier},

keywords = {functor category; analytic functor; artinian functor; artinian conjecture; polynomial functor; polynomial filtration; difference functor; simple functor; Weyl functor},

language = {eng},

number = {3},

pages = {781-805},

publisher = {Association des Annales de l'Institut Fourier},

title = {The structure of the tensor product of $\{\mathbb \{F\}\}_2[-]$ with a finite functor between $\{\mathbb \{F\}\}_2$-vector spaces},

url = {http://eudml.org/doc/75438},

volume = {50},

year = {2000},

}

TY - JOUR

AU - Powell, Geoffrey M. L.

TI - The structure of the tensor product of ${\mathbb {F}}_2[-]$ with a finite functor between ${\mathbb {F}}_2$-vector spaces

JO - Annales de l'institut Fourier

PY - 2000

PB - Association des Annales de l'Institut Fourier

VL - 50

IS - 3

SP - 781

EP - 805

AB - The paper studies the structure of functors $I \otimes F$ in the category of functors from finite dimensional ${\Bbb F}_2$-vector spaces to ${\Bbb F}_2$-vector spaces, where $F$ is a finite functor and $I $ is the injective functor $V \mapsto {\Bbb F}_2^{V^*}$. A detection theorem is proved for sub-functors of such functors, which is the basis of the proof that the functors $I\otimes F$ are artinian of type one.

LA - eng

KW - functor category; analytic functor; artinian functor; artinian conjecture; polynomial functor; polynomial filtration; difference functor; simple functor; Weyl functor

UR - http://eudml.org/doc/75438

ER -

## References

top- [J] G.D. JAMES, The representation theory of the symmetric groups, Lecture Notes in Math., 682 (1978). Zbl0393.20009MR80g:20019
- [J2] G.D. JAMES, The decomposition of tensors over finite fields of prime characteristic, Math. Zeit., 172 (1980), 161-178. Zbl0438.20008MR81h:20015
- [JK] G.D. JAMES, A. KERBER, The Representation Theory of the Symmetric Groups, Ency. Math. Appl., Addison-Wesley, Vol. 16, 1981. Zbl0491.20010MR83k:20003
- [K1] N.J. KUHN, Generic representations of the finite general linear groups and the Steenrod algebra : I, Amer. J. Math., 116 (1993), 327-360. Zbl0813.20049MR95c:55022
- [K2] N.J. KUHN, Generic representations of the finite general linear groups and the Steenrod algebra : II, K-Theory, 8 (1994), 395-426. Zbl0830.20065MR95k:55038
- [K3] N.J. KUHN, Generic representations of the finite general linear groups and the Steenrod algebra : III, K-Theory, 9 (1995), 273-303. Zbl0831.20057MR97c:55026
- [PS] L. PIRIOU, L. SCHWARTZ, Extensions de foncteurs simples, K-theory, 15 (1998), 269-291. Zbl0918.20036MR2000g:20085
- [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. Zbl0928.18004
- [P2] G.M.L. POWELL, Polynomial filtrations and Lannes' T-functor, K-Theory, 13 (1998), 279-304. Zbl0892.55009MR99c:55016
- [P3] G.M.L. POWELL, The structure of Ī⊗Λn in generic representation theory, J. Alg., 194 (1997), 455-466. Zbl0893.55011MR98g:55020
- [P4] G.M.L. POWELL, The structure of the indecomposable injectives in generic representation theory, Trans. Amer. Math. Soc., 350 (1998), 4167-4193. Zbl0903.18006MR98m:18004
- [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. Zbl1160.18305

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.