Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Twisted representation rings and Dirac induction   Extending ideas of twisted equivariant $K$-theory, we construct twisted
versions of the representation rings for Lie superalgebras and Lie supergroups,
built from projective $\Z_{2}$-graded representations with a given cocycle. We
then investigate the pullback and pushforward maps on these representation
rings (and their completions) associated to homomorphisms of Lie superalgebras
and Lie supergroups.
  As an application, we consider the Lie supergroup $\Pi (T^{*}G)$, obtained by
taking the cotangent bundle of a compact Lie group and reversing the parity of
its fibers. An inclusion $H \hookrightarrow G$ induces a homomorphism from the
twisted representation ring of $\Pi(T^{*}H)$ to the twisted representation ring
of $\Pi(T^{*}G)$, which pulls back via an algebraic version of the Thom
isomorphism to give an additive homomorphism from $K_{H}(\mathrm{pt})$ to
$K_{G}(\mathrm{pt})$ (possibly with twistings). We then show that this
homomorphism is in fact Dirac induction, which takes an $H$-module $U$ to the
$G$-equivariant index of the Dirac operator $\dirac \otimes U$ on the
homogeneous space $G/H$ with values in the homogeneous bundle induced by $U$.

23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con