Cox, A.

Erdmann, K.

English

In the study of highest weight categories, the class of Weyl modules Δ(λ) and their 
duals ∇(λ) are of central interest; this is for example motivated by the problem of 
finding the characters of the simple modules. Weyl modules form the building blocks 
for the category [Fscr ](Δ), whose objects have a filtration 
0 = M0 [les ] M1 [les ] … [les ] 
Mi−1 [les ] Mi = M 
with quotients isomorphic to Δ(λ) for various λ. Knowing 
Extr(Δ(λ), Δ(μ)) 
is essential for the understanding of this category.In [3, 13], we determined Ext1 for Weyl modules 
of SL(2, k) and q-GL(2, k) over 
an infinite field k of characteristic p &gt; 0. 
Here we are able to extend these results to 
determine Ext2 for Weyl modules in both these cases (see Theorem 4 · 6). Moreover, 
this also gives Ext2 between any pair of Weyl modules 
Δ(λ), Δ(μ) for q-GL(n, k) 
(where n [ges ] 2) such that both λ and μ have at most two rows or two columns, or 
where they differ by some multiple of a simple root (see Section 7).Consider (for simplicity) polynomial representations of degree d 
for GL(n, k). A 
partition of d which has at most two rows is uniquely determined by the difference 
in the row lengths, which we use as a label for the partition. In this case our main 
result is</jats:p

ANTON COX

KARIN ERDMANN

Crossref

Mathematical Proceedings of the Cambridge Philosophical Society

On Ext2 between Weyl modules for quantum GLn

Cox, A

Erdmann, Karin

Oxford University Research Archive

On Ext(2) between Weyl modules for quantum GL(n)

City Research Online

ORA - Oxford University Research Archive

Erdmann, K

Oxford University Research Archive (ORA)

http://openaccess.city.ac.uk/379/2/coxerd.pdf

On Ext(2) between Weyl modules for quantum GL(n)

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Crossref

Oxford University Research Archive

City Research Online

ORA - Oxford University Research Archive

Oxford University Research Archive (ORA)