3,897 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"
correcte
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
Equivariant Giambelli and determinantal restriction formulas for the Grassmannian
The main result of the paper is a determinantal formula for the restriction
to a torus fixed point of the equivariant class of a Schubert subvariety in the
torus equivariant integral cohomology ring of the Grassmannian. As a corollary,
we obtain an equivariant version of the Giambelli formula.Comment: 16 pages, 3 figures, LaTex, uses epsfig and psfrag; for the revised
version: title changed; Proof of Theorem 3 changed; 3 references added and 1
deleted; other minor change
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