Dirac cohomology and translation functors (CROSBI ID 178045)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Mehdi, Salah ; Pandžić, Pavle
engleski
Dirac cohomology and translation functors
We study the relationship between the Dirac cohomology of a $(\fg, K)$-module $X$ and the Dirac cohomology of a Jantzen-Zuckerman translate of $X$. More precisely, we show that if $X$ is unitary, and if some submodule $X'$ of a translate of $X$ has nonzero Dirac cohomology, then $X$ has nonzero Dirac cohomology. In the course of the proof, we show that the space of harmonic spinors (i.e., the kernel of the Dirac operator) related to $X'$ embeds into a sort of product of harmonic spinors for $X$ and harmonic spinors for the finite-dimensional module used to define the translation. This generalizes results of \cite{; ; ; MP08}; ; ; and \cite{; ; ; MP09}; ; ; .
(g; K)-module; Dirac operator; Dirac cohomology; translation functor.
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