Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On cacti and crystals   In the present work we study actions of various groups generated by
involutions on the category $\mathscr O^{int}_q(\mathfrak g)$ of integrable
highest weight $U_q(\mathfrak g)$-modules and their crystal bases for any
symmetrizable Kac-Moody algebra $\mathfrak g$. The most notable of them are the
cactus group and (yet conjectural) Weyl group action on any highest weight
integrable module and its lower and upper crystal bases. Surprisingly, some
generators of cactus groups are anti-involutions of the Gelfand-Kirillov model
for $\mathscr O^{int}_q(\mathfrak g)$ closely related to the remarkable quantum
twists discovered by Kimura and Oya.

19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex