IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i3p295-d216287.html
   My bibliography  Save this article

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

Author

Listed:
  • Muhammad Fazeel Anwar

    (Department of Mathematics, Sukkur IBA University, Sukkur 65200, Pakistan)

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.

Suggested Citation

  • Muhammad Fazeel Anwar, 2019. "Some Results on the Cohomology of Line Bundles on the Three Dimensional Flag Variety," Mathematics, MDPI, vol. 7(3), pages 1-5, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:295-:d:216287
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/3/295/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/3/295/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:295-:d:216287. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.