Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $D_5^{(1)}$- Geometric Crystal corresponding to the Dynkin spin node
  $i=5$ and its ultra-discretization   Let $g$ be an affine Lie algebra with index set $I = \{0, 1, 2, \cdots , n\}$
and $g^L$ be its Langlands dual. It is conjectured that for each Dynkin node $i
\in I \setminus \{0\}$ the affine Lie algebra $g$ has a positive geometric
crystal whose ultra-discretization is isomorphic to the limit of certain
coherent family of perfect crystals for $g^L$. In this paper we construct a
positive geometric crystal $V(D_5^{(1)})$ in the level zero fundamental spin
$D_5^{(1)}$- module $W(\varpi_5)$. Then we define explicit $0$-action on the
level $l$ known $D_5^{(1)}$- perfect crystal $B^{5, l}$ and show that $\{B^{5,
l}\}_{l \geq 1}$ is a coherent family of perfect crystals with limit $B^{5,
\infty}$. Finally we show that the ultra-discretization of $V(D_5^{(1)})$ is
isomorphic to $B^{5, \infty}$ as crystals which proves the conjecture in this
case.

35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat