The structure of the tensor product of 𝔽 2 [ - ] with a finite functor between 𝔽 2 -vector spaces

Geoffrey M. L. Powell

Annales de l'institut Fourier (2000)

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

Abstract

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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.

How to cite

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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 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

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  1. [J] G.D. JAMES, The representation theory of the symmetric groups, Lecture Notes in Math., 682 (1978). Zbl0393.20009MR80g:20019
  2. [J2] G.D. JAMES, The decomposition of tensors over finite fields of prime characteristic, Math. Zeit., 172 (1980), 161-178. Zbl0438.20008MR81h:20015
  3. [JK] G.D. JAMES, A. KERBER, The Representation Theory of the Symmetric Groups, Ency. Math. Appl., Addison-Wesley, Vol. 16, 1981. Zbl0491.20010MR83k:20003
  4. [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
  5. [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
  6. [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
  7. [PS] L. PIRIOU, L. SCHWARTZ, Extensions de foncteurs simples, K-theory, 15 (1998), 269-291. Zbl0918.20036MR2000g:20085
  8. [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
  9. [P2] G.M.L. POWELL, Polynomial filtrations and Lannes' T-functor, K-Theory, 13 (1998), 279-304. Zbl0892.55009MR99c:55016
  10. [P3] G.M.L. POWELL, The structure of Ī⊗Λn in generic representation theory, J. Alg., 194 (1997), 455-466. Zbl0893.55011MR98g:55020
  11. [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
  12. [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

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