The group ring of GLn(q) and the q-Schur algebra

Mitsuhiro TAKEUCHI

doi:10.2969/jmsj/04820259

The group ring of GL_n(q) and the q-Schur algebra

Mitsuhiro TAKEUCHI

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1996 Volume 48 Issue 2 Pages 259-274

DOI https://doi.org/10.2969/jmsj/04820259

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Published: 1996 Received: December 22, 1992 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: TITLE Details: Wrong : The group ring of GL_n(q) and theq-Schur algebra
Right : The group ring of GL_n(q) and the q-Schur algebra

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) N. Bourbaki, Groupes et algèbres de Lie, Chap. 4-6, Hermann, Paris, 1968.
2) R. Dipper, Polynomial representations of finite general linear groups in non-describing characteristic, Progr. Math., 95 (1991), 343-370.
3) R. Dipper and S. Donkin, Quantum GL_n, Proc. London Math. Soc. (3), 63 (1991), 165-211.
4) R. Dipper and G. James, Representations of Hecke algebras of general linear groups, Proc. London Math. Soc. (3), 52 (1986), 20-52.
5) R. Dipper and G. James, The q-Schur algebra, Proc. London Math. Soc. (3), 59 (1989), 23-50.
6) R. Dipper and G. James, q-Tensor space and q-Weyl modules, Trans. Amer. Math. Soc., 327 (1991), 251-282.
7) J. A. Green, Polynomial representations of GL_n, Lecture Notes in Math., 830, Springer, 1980.
8) N. Iwahori, On the structure of the Hecke algebra of a Chevalley group over a finite field, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 10 (1964), 215-236.
9) G. James, Representations of general linear groups, London Math. Soc. Lecture Note Ser., 94, Cambridge, 1984.
10) G. James, The decomposition matrices of GL_n(q) for n_??_10, Proc. London Math. Soc. (3), 60 (1990), 225-265.

Right : [1] N. Bourbaki, Groupes et algèbres de Lie, Chap. 4-6, Hermann, Paris, 1968.
[2] R. Dipper, Polynomial representations of finite general linear groups in non-describing characteristic, Progr. Math., 95 (1991), 343-370.
[3] R. Dipper and S. Donkin, Quantum GL_n, Proc. London Math. Soc. (3), 63 (1991), 165-211.
[4] R. Dipper and G. James, Representations of Hecke algebras of general linear groups, Proc. London Math. Soc. (3), 52 (1986), 20-52.
[5] R. Dipper and G. James, The q-Schur algebra, Proc. London Math. Soc. (3), 59 (1989), 23-50.
[6] R. Dipper and G. James, q-Tensor space and q-Weyl modules, Trans. Amer. Math. Soc., 327 (1991), 251-282.
[7] J. A. Green, Polynomial representations of GL_n, Lecture Notes in Math., 830, Springer, 1980.
[8] N. Iwahori, On the structure of the Hecke algebra of a Chevalley group over a finite field, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 10 (1964), 215-236.
[9] G. James, Representations of general linear groups, London Math. Soc. Lecture Note Ser., 94, Cambridge, 1984.
[10] G. James, The decomposition matrices of GL_n(q) for n≤10, Proc. London Math. Soc. (3), 60 (1990), 225-265.

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