Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonstandard Drinfeld-Sokolov reduction   Subject to some conditions, the input data for the Drinfeld-Sokolov
construction of KdV type hierarchies is a quadruplet $(\A,\Lambda, d_1, d_0)$,
where the $d_i$ are $\Z$-gradations of a loop algebra $\A$ and $\Lambda\in \A$
is a semisimple element of nonzero $d_1$-grade. A new sufficient condition on
the quadruplet under which the construction works is proposed and examples are
presented. The proposal relies on splitting the $d_1$-grade zero part of $\A$
into a vector space direct sum of two subalgebras. This permits one to
interpret certain Gelfand-Dickey type systems associated with a nonstandard
splitting of the algebra of pseudo-differential operators in the
Drinfeld-Sokolov framework.

10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg