Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalised Springer correspondence for Z/m-graded Lie algebras   Let $G$ be a simple simply connected complex algebraic group and let
$\mathfrak{g}_*$ be a $\mathbf{Z}/m$-grading on its Lie algebra $\mathfrak{g}$.
In a recent series of articles, G. Lusztig and Z. Yun, studied the
classification of simple $G_0$-equivariant perverse sheaves on the nilpotent
cone of $\mathfrak{g}_i$ for $i\in \mathbf{Z}/m$, where $G_0$ is the
exponentiation of the degree zero piece $\mathfrak{g}_0$. They proved a
decomposition of the equivariant derived category of $\ell$-adic sheaves on the
nilpotent cone of $\mathfrak{g}_i$ into blocks, each generated by a certain
cuspidal local system via {\itshape spiral inductions}. We prove a conjecture
of them, which predicts the bijectivity of a map from 1) the set of simple
perverse sheaves in a fixed block to 2) the set of simple modules of a block of
a (trigonometric) degenerate double affine Hecke algebra (dDAHA). This is a
dDAHA analogue of the Deligne--Langlands correspondence for affine Hecke
algebras proven by Kazhdan--Lusztig. Our results generalise a previous work of
E. Vasserot, where the perverse sheaves in the principal block were considered.

7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics