Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A combinatorial study of affine Schubert varieties in affine
  Grassmannian   Let $\overline{\mathtt{X}}_\lambda$ be the closure of the $\mathtt{I}$-orbit
$\mathtt{X}_\lambda$ in the affine Grassmanian $\mathtt{Gr}$ of a simple
algebraic group $G$ of adjoint type, where $\mathtt{I}$ is the Iwahori group
and $\lambda$ is a coweight of $G$. We find a simple algorithm which describes
the set $\Psi(\lambda)$ of all $\mathtt{I}$-orbits in
$\overline{\mathtt{X}}_\lambda$ in terms of coweights. We introduce
$R$-operators (associated to positive roots) on the coweight lattice of $G$,
which exactly describe the closure relation of $\mathtt{I}$-orbits. These
operators satisfy Braid relations generically on the coweight lattice. We also
establish a duality between the set $\Psi(\lambda)$ and the weight system of
the level one affine Demazure module $\hat{\mathscr{D}}_\lambda$ of
$^L\tilde{\mathfrak{g}}$ indexed by $\lambda$, where $^L\tilde{\mathfrak{g}}$
is the affine Kac-Moody algebra dual to the affine Kac-Moody Lie algebra
$\tilde{\mathfrak{g}}$ associated to the Lie algebra $\mathfrak{g}$ of $G$.

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The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
28
The categories of this paper are: alg-geom