Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lefschetz theory for exterior algebras and fermionic diagonal
  coinvariants   Let $W$ be an irreducible complex reflection group acting on its reflection
representation $V$. We consider the doubly graded action of $W$ on the exterior
algebra $\wedge (V \oplus V^*)$ as well as its quotient $DR_W := \wedge (V
\oplus V^*)/ \langle \wedge (V \oplus V^*)^{W}_+ \rangle$ by the ideal
generated by its homogeneous $W$-invariants with vanishing constant term. We
describe the bigraded isomorphism type of $DR_W$; when $W = \mathfrak{S}_n$ is
the symmetric group, the answer is a difference of Kronecker products of
hook-shaped $\mathfrak{S}_n$-modules. We relate the Hilbert series of $DR_W$ to
the (type A) Catalan and Narayana numbers and describe a standard monomial
basis of $DR_W$ using a variant of Motzkin paths. Our methods are type-uniform
and involve a Lefschetz-like theory which applies to the exterior algebra
$\wedge (V \oplus V^*)$.

32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph