arXiv Open Access 2019

Dual pairs in the Pin-group and duality for the corresponding spinorial representation

Clément Guérin Gang Liu Allan Merino

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Abstrak

In this paper, we give a complete picture of Howe correspondence for the setting ($O(E, b), Pin(E, b), Π$), where $O(E, b)$ is an orthogonal group (real or complex), $Pin(E, b)$ is the two-fold Pin-covering of $O(E, b)$, and $Π$ is the spinorial representation of $Pin(E, b)$. More precisely, for a dual pair ($G, G'$) in $O(E, b)$, we determine explicitly the nature of its preimages $(\tilde{G}, \tilde{G'})$ in $Pin(E, b)$, and prove that apart from some exceptions, $(\tilde{G}, \tilde{G'})$ is always a dual pair in $Pin(E, b)$; then we establish the Howe correspondence for $Π$ with respect to $(\tilde{G}, \tilde{G'})$.

Topik & Kata Kunci

math.RT

Penulis (3)

Clément Guérin

Gang Liu

Allan Merino

Format Sitasi

APA MLA BibTeX

Guérin, C., Liu, G., Merino, A. (2019). Dual pairs in the Pin-group and duality for the corresponding spinorial representation. https://arxiv.org/abs/1907.09093

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Informasi Jurnal

Tahun Terbit: 2019
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓