engleski

Dirac induction for Harish-Chandra modules

We introduce new notions of Dirac cohomology and homology of a Harish-Chandra module $X$. If $X$ is unitary or finite-dimensional then these new notions both coincide with the previously studied version of Dirac cohomology from \cite{; ; ; V}; ; ; and \cite{; ; ; HP}; ; ; . The new notions have certain advantages. Notably, if $X$ is irreducible and has nonzero Dirac cohomology (respectively homology), then $X$ is uniquely determined by its Dirac cohomology (respectively homology). Furthermore, one can define adjoint functors that we call Dirac induction functors. We study basic properties of these functors and we calculate their result explicitly in some examples.

Harish-Chandra module; Dirac cohomology; Dirac indcution

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