4,924 research outputs found
Initial ideals of tangent cones to Schubert varieties in orthogonal Grassmannians
We compute the initial ideals, with respect to certain conveniently chosen
term orders, of ideals of tangent cones at torus fixed points to Schubert
varieties in orthogonal Grassmannians. The initial ideals turn out to be
square-free monomial ideals and therefore Stanley-Reisner face rings of
simplicial complexes. We describe these complexes. The maximal faces of these
complexes encode certain sets of non-intersecting lattice paths.Comment: 36 pages, 3 figures; for version 2: error in definition of "new form"
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The cell lineage of the muscles of the Drosophila head
Using a cell marker mutation the cell lineage of the muscles of the Drosophila head are traced out. Three sets of muscles separated by lineage restrictions are observed, even when cells are marked as early as the blastoderm stage. Each set underlies the derivatives of one of the three pairs of imaginal discs which differentiate to form the epidermis of the adult head. Clones of the homoeotic mutation engrailed (en^10) were apparently normal in the muscles of the head. The muscle clone frequency, at the blastoderm stage, in each hemisegment of the fly is similar, indicating an equal partitioning of cells during segmentation
Stability of the Chari-Pressley-Loktev bases for local Weyl modules of
We prove stability of the Chari-Pressley-Loktev bases for natural inclusions
of local Weyl modules of the current algebra . These modules being
known to be Demazure submodules in the level 1 representations of the affine
Lie algebra , we obtain, by passage to the direct limit, bases
for the level 1 representations themselves.Comment: 20 pages; minor revision
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