Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hilbert functions of points on Schubert varieties in Orthogonal
  Grassmannians   A solution is given to the following problem: how to compute the
multiplicity, or more generally the Hilbert function, at a point on a Schubert
variety in an orthogonal Grassmannian. Standard monomial theory is applied to
translate the problem from geometry to combinatorics. The solution of the
resulting combinatorial problem forms the bulk of the paper. This approach has
been followed earlier to solve the same problem for the Grassmannian and the
symplectic Grassmannian.
  As an application, we present an interpretation of the multiplicity as the
number of non-intersecting lattice paths of a certain kind.
  Taking the Schubert variety to be of a special kind and the point to be the
"identity coset," our problem specializes to a problem about Pfaffian ideals
treatments of which by different methods exist in the literature. Also
available in the literature is a geometric solution when the point is a
"generic singularity."

12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th