Higher extensions between modules for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:msub><mml:mi mathvariant="normal">SL</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>

Parker, Alison E.

doi:10.1016/j.aim.2006.05.015

Cited by 21 publications

(3 citation statements)

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“…In particular, if s ≥ 1, then λ lies in the same block as 2p s only if either a is even and i = 0, or if a is odd and i = p − 2. In this paper we apply various recursive formulas developed by Parker [4] for computing the higher extension groups between certain classes of rational SL 2 -modules. In order to simplify the statements of some formulas, we sometimes include more summands than are written in the formulas' original statements.…”

Section: Preliminariesmentioning

confidence: 99%

“…especially the second-to-last paragraph on page 394), this spectral sequence stabilizes at the E 2 -page. Specifically, taking i = a = 0 and N = (gl 2 ) (r−1) in the last spectral sequence on page 394 of [4] if p ≥ 3, or in the second spectral sequence on page 395 of [4] if p = 2, one obtains for q ≥ 0 the vector space decomposition…”

Section: Existence Of Universal Extension Classes For Slmentioning

confidence: 99%

“…Using Parker's recursive formulas for computing higher extensions between modules for SL 2 , we also obtain the fact that the universal extension classes for GL 2 are unique up to scalar multiples (Theorem 4.5); this is a sharper result than the existence statement given by van der Kallen. Most of the notation in this article is standard, and can be found for example in [3,4].…”

Section: Introductionmentioning

confidence: 99%

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Universal Extension Classes for GL 2

Drupieski

2014

Algebr Represent Theor

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In this note we give a new existence proof for the universal extension classes for GL 2 previously constructed by Friedlander and Suslin via the theory of strict polynomial functors. The key tool in our approach is a calculation of Parker showing that, for suitable choices of coefficient modules, the Lyndon-Hochschild-Serre spectral sequence for SL 2 relative to its first Frobenius kernel stabilizes at the E 2 -page. Consequently, we obtain a new proof that if G is an infinitesimal subgroup scheme of GL 2 , then the cohomology ring H • (G, k) of G is a finitely-generated noetherian k-algebra.

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Section: Preliminariesmentioning

confidence: 99%

Section: Existence Of Universal Extension Classes For Slmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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