Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Green polynomials of Weyl groups, elliptic pairings, and the extended
  Dirac index   We provide a direct connection between Springer theory, via Green
polynomials, the irreducible representations of the pin cover $\wti W$, a
certain double cover of the Weyl group $W$, and an extended Dirac operator for
graded Hecke algebras. Our approach leads to a new and uniform construction of
the irreducible genuine $\wti W$-characters. In the process, we give a
construction of the action by an outer automorphism of the Dynkin diagram on
the cohomology groups of Springer theory, and we also introduce a $q$-elliptic
pairing for $W$ with respect to the reflection representation $V$. These
constructions are of independent interest. The $q$-elliptic pairing is a
generalization of the elliptic pairing of $W$ introduced by Reeder, and it is
also related to S. Kato's notion of (graded) Kostka systems for the semidirect
product $A_W=\bC[W]\ltimes S(V)$.

16
The categories of this paper are: stat
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph