Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Parity of Lusztig's Restriction Functor and Green's Formula   Our investigation in the present paper is based on three important results.
(1) In [12], Ringel introduced Hall algebra for representations of a quiver
over finite fields and proved the elements corresponding to simple
representations satisfy the quantum Serre relation. This gives a realization of
the nilpotent part of quantum group if the quiver is of finite type. (2) In
[4], Green found a homological formula for the representation category of the
quiver and equipped Ringel's Hall algebra with a comultiplication. The generic
form of the composition subalgebra of Hall algebra generated by simple
representations realizes the nilpotent part of quantum group of any type. (3)
In [9], Lusztig defined induction and restriction functors for the perverse
sheaves on the variety of representations of the quiver which occur in the
direct images of constant sheaves on flag varieties, and he found a formula
between his induction and restriction functors which gives the comultiplication
as algebra homomorphism for quantum group. In the present paper, we prove the
formula holds for all semisimple complexes with Weil structure. This
establishes the categorification of Green's formula.

9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
3
The categories of this paper are: physics