An application of topology to computing the cohomology of Young modules for the symmetric group
Homological Methods in Representation Theory
April 01, 2008 02:00 PM to 03:00 PM
Speakers:
Hemmer, David
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Abstract: |
We will discuss recent joint work with F. Cohen and D. Nakano
which allows us to compute cohomology of Young modules for the symmetric
group, often in all possible degrees. The methods are strong enough to
determine, in any characteristic, which Young modules have vanishing
cohomology in all degrees, and there are many of them! We can also give
explicit formulas for low degree cohomology and arbitrary symmetric groups.
We demonstrate a stability result for cohomology which is reminiscent of
generic cohomology for algebraic groups. We believe this is the first
theorem for the symmetric group involving multiplying a partition by "p",
something analogous to a Frobenius twist for symmetric groups! Finally we
show that knowledge just the space of homomorphisms between two Young
modules is enough to determine cohomology in all degrees. |
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Lecture #12711
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