| Title:
|
Structure of the kernel of higher spin Dirac operators (English) |
| Author:
|
Plechšmíd, Martin |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
42 |
| Issue:
|
4 |
| Year:
|
2001 |
| Pages:
|
665-680 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Polynomials on $\Bbb R^n$ with values in an irreducible $\operatorname{Spin}_n$-module form a natural representation space for the group $\operatorname{Spin}_n$. These representations are completely reducible. In the paper, we give a complete description of their decompositions into irreducible components for polynomials with values in a certain range of irreducible modules. The results are used to describe the structure of kernels of conformally invariant elliptic first order systems acting on maps on $\Bbb R^n$ with values in these modules. (English) |
| Keyword:
|
conformally invariant differential operators |
| Keyword:
|
generalized (higher-spin) Dirac operators |
| Keyword:
|
representations of spin-groups |
| Keyword:
|
Littlewood-Richardson rule |
| MSC:
|
32A50 |
| MSC:
|
43A65 |
| MSC:
|
53A30 |
| MSC:
|
53A55 |
| MSC:
|
53C27 |
| idZBL:
|
Zbl 1090.53502 |
| idMR:
|
MR1883376 |
| . |
| Date available:
|
2009-01-08T19:17:35Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119283 |
| . |
| Reference:
|
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| . |
