Access the full text.
Sign up today, get DeepDyve free for 14 days.
References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.
RATIONALLY INJECTIVE MODULES FOR SEMISIMPLE ALGEBRAIC GROUPS AS DIRECT LIMITS STEPHEN DONKIN In this note we give a short, simple minded proof of the direct limit theorem, a version of which appears as Proposition 2 of [1], as Theorem 6.2 of [3] and appears in §4.7 of [9] . This was conjectured to be true by J. E. Humphreys on the evidence of Winter's treatment of the two dimensional special linear group in [10]. We assume the notation of [8], in particular G denotes a simply connected, semisimple algebraic group over an algebraically closed field K of prime characteristic p, u the m-th hyperalgebra of G for a positive integer m and L(v) the simple rational G module of highest weight v. Let V be a left u module. By a G structure on V we mean a rational G module W such that the restriction of W to u is isomorphic to V. Of course there may not be a G structure on V and even if one does exist it may not be unique (see [4] however). Our theorem asserts that if, for various vel^w e have a G structure Q(y) on Q(l, v) then certain direct
Bulletin of the London Mathematical Society – Wiley
Published: Mar 1, 1980
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.