Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Flag manifolds over semifields   In this paper, we develop the theory of flag manifold over a semifield for
any Kac-Moody root datum. We show that the flag manifold over a semifield
admits a natural action of the monoid over that semifield associated with the
Kac-Moody datum and admits a cellular decomposition. This extends the previous
work of Lusztig, Postnikov, Rietsch and others on the totally nonnegative flag
manifolds (of finite type) and the work of Lusztig, Speyer, Williams on the
tropical flag manifolds (of finite type). As a by-product, we prove a
conjecture of Lusztig on the duality of totally nonnegative flag manifold of
finite type.

36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph