Classification of differential symmetry breaking operators for differential forms

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• 作者：Toshiyuki Kobayashi^a ; ^{toshi@ms.u-tokyo.ac.jp" class="auth_mail" title="E-mail the corresponding author} ; Toshihisa Kubo^b ; ^{toskubo@ms.u-tokyo.ac.jp" class="auth_mail" title="E-mail the corresponding author} ; Michael Pevzner^c ; ^{pevzner@univ-reims.fr" class="auth_mail" title="E-mail the corresponding author}
• 刊名：Comptes Rendus Mathematique
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：354
• 期：7
• 页码：671-676
• 全文大小：270 K

文摘

We give a complete classification of conformally covariant differential operators between the spaces of differential i  -forms on the sphere Sⁿ$S^n$ and j  -forms on the totally geodesic hypersphere Sⁿ⁻¹$S^{n-1}$ by analyzing the restriction of principal series representations of the Lie group O(n+1,1)$O(n+1,1)$. Further, we provide explicit formulæ for these matrix-valued operators in the flat coordinates and find factorization identities for them.