315 research outputs found
Poitou-Tate without restrictions on the order
The Poitou-Tate sequence relates Galois cohomology with restricted
ramification of a finite Galois module over a global field to that of the
dual module under the assumption that is a unit away from the allowed
ramification set. We remove the assumption on by proving a generalization
that allows arbitrary "ramification sets" that contain the archimedean places.
We also prove that restricted products of local cohomologies that appear in the
Poitou-Tate sequence may be identified with derived functor cohomology of an
adele ring. In our proof of the generalized sequence we adopt this derived
functor point of view and exploit properties of a natural topology carried by
cohomology of the adeles.Comment: 28 pages; final version, to appear in Mathematical Research Letter
Demazure crystals, Kirillov-Reshetikhin crystals, and the energy function
It has previously been shown that, at least for non-exceptional Kac-Moody Lie
algebras, there is a close connection between Demazure crystals and tensor
products of Kirillov-Reshetikhin crystals. In particular, certain Demazure
crystals are isomorphic as classical crystals to tensor products of
Kirillov-Reshetikhin crystals via a canonically chosen isomorphism. Here we
show that this isomorphism intertwines the natural affine grading on Demazure
crystals with a combinatorially defined energy function. As a consequence, we
obtain a formula of the Demazure character in terms of the energy function,
which has applications to Macdonald polynomials and q-deformed Whittaker
functions.Comment: 35 pages. v2: minor revisions, including several new examples and
reference
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