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Mathematics 2019, 7(3), 295; https://doi.org/10.3390/math7030295

Some Results on the Cohomology of Line Bundles on the Three Dimensional Flag Variety

Department of Mathematics, Sukkur IBA University, Sukkur 65200, Pakistan
Received: 1 March 2019 / Revised: 14 March 2019 / Accepted: 14 March 2019 / Published: 22 March 2019
(This article belongs to the Special Issue Lie Theory and Its Applications)
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Abstract

Let k be an algebraically closed field of prime characteristic and let G be a semisimple, simply connected, linear algebraic group. It is an open problem to find the cohomology of line bundles on the flag variety G / B , where B is a Borel subgroup of G. In this paper we consider this problem in the case of G = S L 3 ( k ) and compute the cohomology for the case when λ , α = p n a 1 , ( 1 a p , n > 0 ) or λ , α = p n r , ( r 2 , n 0 ) . We also give the corresponding results for the two dimensional modules N α ( λ ) . These results will help us understand the representations of S L 3 ( k ) in the given cases. View Full-Text
Keywords: representation theory; algebraic groups; cohomology; line bundles representation theory; algebraic groups; cohomology; line bundles
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Anwar, M.F. Some Results on the Cohomology of Line Bundles on the Three Dimensional Flag Variety. Mathematics 2019, 7, 295.

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