کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6425480 | 1633803 | 2015 | 57 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Branching laws for Verma modules and applications in parabolic geometry. I
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Branching laws for Verma modules and applications in parabolic geometry. I Branching laws for Verma modules and applications in parabolic geometry. I](/preview/png/6425480.png)
چکیده انگلیسی
We initiate a new study of differential operators with symmetries and combine this with the study of branching laws for Verma modules of reductive Lie algebras. By the criterion for discretely decomposable and multiplicity-free restrictions of generalized Verma modules (T. Kobayashi (2012) [22]), we are brought to natural settings of parabolic geometries for which there exist unique equivariant differential operators to submanifolds. Then we apply a new method (F-method) relying on the Fourier transform to find singular vectors in generalized Verma modules, which significantly simplifies and generalizes many preceding works. In certain cases, it also determines the Jordan-Hölder series of the restriction for singular parameters. The F-method yields an explicit formula of such unique operators, for example, giving an intrinsic and new proof of Juhl's conformally invariant differential operators (Juhl (2009) [16]) and its generalizations to spinor bundles. This article is the first in the series, and the next ones include their extension to curved cases together with more applications of the F-method to various settings in parabolic geometries.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 285, 5 November 2015, Pages 1796-1852
Journal: Advances in Mathematics - Volume 285, 5 November 2015, Pages 1796-1852
نویسندگان
Toshiyuki Kobayashi, Bent Ãrsted, Petr Somberg, VladimÃr SouÄek,