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Aspects of characteristic-free representation theory of GLn, and some applications to intertwining numbers

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Topics in Computational Algebra
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Abstract

Characteristic-free representation theory has been studied by many people over the past fifteen years in many different ways for many different reasons. In the mid-seventies, Carter and Lusztig [6] defined the Weyl modules for the general linear group over any field, independent of characteristic. Towber, a little later [9], defined the Schur and Weyl modules for GLn over an arbitrary commutative ring. Using standard monomial theory, Lakshmibai, Musili and Seshadri [8] defined the Schur modules for the classical groups over any commutative ring.

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Bibliography

  1. K. Akin and D. A. Buchsbaum, Characteristic-free representation theory of the general linear group. Adv. in Math. 58 (1985), 149–200.

    Article  MathSciNet  MATH  Google Scholar 

  2. K. Akin and D. A. Buchsbaum, Characteristic-free representation theory of the general linear group, II: Eomological considerations. Adv. in Math. 72 (1988), 171–210.

    Article  MathSciNet  MATH  Google Scholar 

  3. K. Akin and D. A. Buchsbaum, Characteristic-free realizations of the Giambelli and Jacobi-Trudi determinantal identities. Proc. of K.I.T. Workshop on Algebra and Toplogy, (1987), 1–19.

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  4. K. Akin and D. A. Buchsbaum, Representations, resolutions and intertwining numbers. Commutative Algebra: Proc. of a microprogram held at MSRI June 15–July 2, 1987. (1989), 1–19.

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  5. K. Akin, D. A. Buchsbaum, and J. Weyman, Schur functors and Schur complexes. Adv. in Math. 44 (1982), 207–278.

    Article  MathSciNet  MATH  Google Scholar 

  6. R. V. Carter and G. Lusztig, On the modular representations of the general linear and symmetric groups. Math. Z. 136 (1974), 193–242.

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  7. J. A. Green, Polynomial Representations of GLn. Lectures Notes in Mathematics, No. 830, Springer-Verlag,, (1980).

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  8. V. Lakshmibai, C. Musili, and C. S. Seshadri, Cohomology of line bundles on G/B. Ann. Sci. École Norm. Sup. 7 (1974), 89–138.

    Google Scholar 

  9. J. Towber, Two new functors from modules to algebras. J. Algebra 47 (1977), 80–109.

    Article  MathSciNet  MATH  Google Scholar 

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© 1990 Springer Science+Business Media Dordrecht

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Buchsbaum, D.A. (1990). Aspects of characteristic-free representation theory of GLn, and some applications to intertwining numbers. In: Cattaneo, G.M.P., Strickland, E. (eds) Topics in Computational Algebra. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3424-8_10

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  • DOI: https://doi.org/10.1007/978-94-011-3424-8_10

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