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by J.A. Green
Download Polynomial Representations of GL_n fb2
  • Author:
    J.A. Green
  • ISBN:
    3540102582
  • ISBN13:
    978-3540102588
  • Genre:
  • Publisher:
    Springer (April 3, 2008)
  • Pages:
    128 pages
  • Language:
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    1129 kb
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The ?rst part is a corrected version of the original text, formatted A in LT X, and retaining the original numbering of sections, equations, etc.

The ?rst part is a corrected version of the original text, formatted A in LT X, and retaining the original numbering of sections, equations, etc. E The second is an Appendix, which is largely independent of the ?rst part, but aL(n,r),de?nedbyP. Littelmann,whichisanalogous to the Schur algebra S(n,r). It is hoped that, in the future, there will be a structure theory of L(n,r) rather like that which underlies the construction of Kac-Moody Lie algebras. Springer Science & Business Media, 30 нояб.

The second half is an Appendix, and can be read independently of the first.

Polynomial Representations of Gln book. Polynomial Representations of GL n: with an Appendix on Schensted Correspondence and Littelmann Paths (Lecture Notes in Mathematics). 0387102582 (ISBN13: 9780387102580).

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Polynomial representations of GL n(K): The Schur algebra. . eights and characters. Описание: This book provides a general introduction to modern mathematical aspects in computing with multivariate polynomials and in solving algebraic systems.

Polynomial representations of GL n(K): The Schur algebra. he module D {lambda, K. he Carter-Lusztig modules V {lambda, K. epresentation theory of the symmetric group. Appendix on Schensted correspondence and Littelmann paths by K. Erdmann, J. A. Green and M. Schocker: A. Introduction. B. The Schensted process. C. Schensted and Littelmann.

Polynomial representations of general linear groups can be identied with mod-ules over Schur algebras. This follows from work of Schur for the eld of complex numbers and has been extended to innite elds by Green. The situation for nite elds seems to be less clear. In fact, Benson and Doty pointed out that Schur-Weyl duality may fail if the eld is too small. For any commutative ring k and any pair n, d of natural numbers, there is a canonical functor from modules over the Schur algebra Sk(n, d) to degree d polyno-mial representations of GLk(n).

In physical science and mathematics, Legendre polynomials (named after Adrien-Marie Legendre, who discovered them in 1782) are a system of complete and orthogonal polynomials, with a vast number of mathematical properties, and numerous applications.

This establishes and explains certain repeating patterns in decomposition matrices of general linear and symmetric groups. We approach this via polynomial representations of the general linear groups GL n (K) or equivalently via Schur algebras. This allows realizing l representations of s(2) in the polynomial space that are in one-to-one correspondence with usual matrices of an appropriate dimension.