Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Torus actions, localization and induced representations on cohomology   This note is motivated by the problem of understanding Springer's remarkable
action of the Weyl group $W=N_G(T)/T$ of a semi-simple complex linear algebraic
group $G$, with maximal torus $T$, on the cohomology algebra of an arbitrary
Springer variety in the flag variety of $G$ from the viewpoint of torus
actions. Continuing the work [CK] which gave a sufficient condition for a group
$\mathcal{W}$ acting on the fixed point set of an algebraic torus action
$(S,X)$ on a complex projective variety $X$ to lift to a representation of
$\mathcal{W}$ on the cohomology algebra $H^*(X)$ (over $\mathbb{C}$), we
describe when the representation on $H^*(X)$ is equivalent to the
representation of $\mathcal{W}$ on the cohomology $H^*(X^S)$ of the fixed point
set. As a consequence of this theorem, we give a simple proof in type $A$ of
the Alvis-Lusztig-Treumann Theorem, which describes Springer's representation
of $W$ for Springer varieties corresponding to nilpotents in a Levi subalgebra
of Lie$(G)$. In the final two sections, we describe the local structure of the
moment graph $\mathfrak{M}(X)$ of a special torus action $(S,X)$, and we also
show that if a finite group $\mathcal{W}$ acts on the moment graph of $X$, then
$\mathcal{W}$ induces pair of actions on $H^*(X)$, namely the left and right or
dot and star actions of Knutson [Knu] and Tymoczko [Tym] respectively. In
particular, $W$ acts on the moment (or Bruhat) graph $\mathfrak{M}(G/P)$ of
$(T,G/P)$ for any parabolic $P$ in $G$ containing $T$, and the right action of
$W$ on $H^*(G/P)$ is an induced representation. Furthermore, we show the left
action of $W$ on $H^*(G/P)$ is trivial.

0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an