Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conormal Varieties on the Cominuscule Grassmannian   Let $G$ be a simply connected, almost simple group over an algebraically
closed field $\mathbf k$, and $P$ a maximal parabolic subgroup corresponding to
omitting a cominuscule root. We construct a compactification
$\phi:T^*G/P\rightarrow X(u)$, where $X(u)$ is a Schubert variety corresponding
to the loop group $LG$. Let $N^*X(w)\subset T^*G/P$ be the conormal variety of
some Schubert variety $X(w)$ in $G/P$; hence we obtain that the closure of
$\phi(N^*X(w))$ in $X(u)$ is a $B$-stable compactification of $N^*X(w)$. We
further show that this compactification is a Schubert subvariety of $X(u)$ if
and only if $X(w_0w)\subset G/P$ is smooth, where $w_0$ is the longest element
in the Weyl group of $G$. This result is applied to compute the conormal fibre
at the zero matrix in any determinantal variety.

26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat