Tensor Products of Fundamental Representations
Canadian journal of mathematics, Tome 40 (1988) no. 3, pp. 633-648
Voir la notice de l'article provenant de la source Cambridge University Press
Let G be a reductive group over a field of characteristic zero. Fix a Borel subgroup B of G which contains a maximal torus T. For each dominant weight X we have an irreducible representation V(X) of G with highest weight X. For two dominant representation X 1 and X 2 we have a decomposition This decomposition is determined by the element of the group ring of the group of characters of T.The objective of this paper is to compute r(X 1, X 2) for all pairs X 1 and X 2 of fundamental weights. This will be used to compute the equations for cones over homogeneous spaces. This problem immediately reduces to the case when G has simple type; An, Bn, Cn, Dn , E 6, E 7, E 8, F 4 and G 2. We will give complete details for the classical types. For the case An we will work with GLn .
Kempf, George; Ness, Linda. Tensor Products of Fundamental Representations. Canadian journal of mathematics, Tome 40 (1988) no. 3, pp. 633-648. doi: 10.4153/CJM-1988-027-1
@article{10_4153_CJM_1988_027_1,
author = {Kempf, George and Ness, Linda},
title = {Tensor {Products} of {Fundamental} {Representations}},
journal = {Canadian journal of mathematics},
pages = {633--648},
year = {1988},
volume = {40},
number = {3},
doi = {10.4153/CJM-1988-027-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1988-027-1/}
}
TY - JOUR AU - Kempf, George AU - Ness, Linda TI - Tensor Products of Fundamental Representations JO - Canadian journal of mathematics PY - 1988 SP - 633 EP - 648 VL - 40 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1988-027-1/ DO - 10.4153/CJM-1988-027-1 ID - 10_4153_CJM_1988_027_1 ER -
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