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Dirac cohomology and translation functors (CROSBI ID 178045)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Mehdi, Salah ; Pandžić, Pavle Dirac cohomology and translation functors // Journal of algebra, 375 (2013), 328-336. doi: 10.1016/j.jalgebra.2012.11.022

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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Podaci o izdanju

375

2013.

328-336

objavljeno

0021-8693

10.1016/j.jalgebra.2012.11.022

Povezanost rada

Matematika

Poveznice
Indeksiranost