Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Barbasch-Sahi algebras and Dirac cohomology   We define a class of algebras which are distinguished by a PBW property and
an orthogonality condition, and which we call Hopf-Hecke algebras, since they
generalize the Drinfeld Hecke algebras defined by Drinfeld. In the course of
studying the orthogonality condition and in analogy to the orthogonal group we
show the existence of a pin cover for cocommutative Hopf algebras over
$\mathbb{C}$ with an orthogonal module or, more generally, pointed
cocommutative Hopf algebras over a field of characteristic $0$ with an
orthogonal module.
  Following the suggestion of Dan Barbasch and Siddhartha Sahi, we define a
Dirac operator and Dirac cohomology for modules of Hopf-Hecke algebras,
generalizing those concepts for connected semisimple Lie groups, graded affine
Hecke algebras and symplectic reflection algebras. Using the pin cover, we
prove a general theorem for a class of Hopf-Hecke algebras which we call
Barbasch-Sahi algebras, which relates the central character of an irreducible
module with non-vanishing Dirac cohomology to the central characters occurring
in its Dirac cohomology, generalizing a result called "Vogan's conjecture" for
connected semisimple Lie groups, analogous results for graded affine Hecke
algebras and for symplectic reflection algebras and Drinfeld Hecke algebras.

35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn