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This booklet is a compilation of numerous works from well-recognized figures within the box of illustration idea. The presentation of the subject is exclusive in delivering numerous varied issues of view, which may still makethe publication very important to scholars and specialists alike. provides numerous various issues of view on key issues in illustration idea, from the world over identified specialists within the box
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Extra info for Algebraic and Analytic Methods in Representation Theory (Perspectives in Mathematics)
The r t h Frobenius morphism on X is the morphism x x given by F~:(A)" X ( A ) X ~ ) X ( A where "yr"A ~ (-~)) A (-r) is the k-algebra homomorphism that takes a into a p~, a C A . W h e n we apply this to G, we obtain in particular the Frobenius hom o m o r p h i s m F~" G --~ G (r). This is clearly a homomorphism of algebraic groups. 3 Gr - Ker(F~). , of the subgroups T, B, U of G. From now on, we shall assume that all our groups are defined over Fp C k. Since F is the identity on Fp, this assumption implies that G (r) = G for all r.
APW] H. H. Andersen, P. Polo, and K. Wen, Representations of quantum algebras, Invent. Math. 104 (1991), 1-59. [Bo] R. Bott, Homogeneous vector bundles, Ann. of Math. (2), 66 (1957), 203-248. [Cu] C. W. Curtis, Representations of Lie algebras of classical type with applications to linear groups, J. Math. Mech. 9 (1960), 307-326. [De] M, Demazure, A very simple proof of Bott's theorem, Invent. Math. 33 (1976), 271-272. 50 H. H. Andersen [Do] S. Donkin, Rational representations of algebraic groups, Lecture Notes in Mathematics 1140, Springer-Verlag, 1985.
Of Math. (2), 66 (1957), 203-248. [Cu] C. W. Curtis, Representations of Lie algebras of classical type with applications to linear groups, J. Math. Mech. 9 (1960), 307-326. [De] M, Demazure, A very simple proof of Bott's theorem, Invent. Math. 33 (1976), 271-272. 50 H. H. Andersen [Do] S. Donkin, Rational representations of algebraic groups, Lecture Notes in Mathematics 1140, Springer-Verlag, 1985. [Ha] R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics 52, Springer-Verlag, 1977. [Hull J.