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

Department of Mathematics, Sukkur IBA University, Sukkur 65200, Pakistan
Mathematics 2019, 7(3), 295; https://doi.org/10.3390/math7030295
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)
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
MDPI and ACS Style

Anwar, M.F. Some Results on the Cohomology of Line Bundles on the Three Dimensional Flag Variety. Mathematics 2019, 7, 295. https://doi.org/10.3390/math7030295

AMA Style

Anwar MF. Some Results on the Cohomology of Line Bundles on the Three Dimensional Flag Variety. Mathematics. 2019; 7(3):295. https://doi.org/10.3390/math7030295

Chicago/Turabian Style

Anwar, Muhammad F. 2019. "Some Results on the Cohomology of Line Bundles on the Three Dimensional Flag Variety" Mathematics 7, no. 3: 295. https://doi.org/10.3390/math7030295

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