Heisenberg Parabolic Subgroups of Exceptional Non-Compact <i>G</i><sub>2(2)</sub> and Invariant Differential Operators
In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebra <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi&...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-03-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/14/4/660 |
| _version_ | 1797409245190160384 |
|---|---|
| author | V.K. Dobrev |
| author_facet | V.K. Dobrev |
| author_sort | V.K. Dobrev |
| collection | DOAJ |
| description | In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebra <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mrow><mn>2</mn><mo>(</mo><mn>2</mn><mo>)</mo></mrow></msub></semantics></math></inline-formula>. We use both the minimal and the maximal Heisenberg parabolic subalgebras. We give the main multiplets of indecomposable elementary representations. This includes the explicit parametrization of the intertwining differential operators between the ERs. These are new results applicable in all cases when one would like to use <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mrow><mn>2</mn><mo>(</mo><mn>2</mn><mo>)</mo></mrow></msub></semantics></math></inline-formula> invariant differential operators. |
| first_indexed | 2024-03-09T04:11:31Z |
| format | Article |
| id | doaj.art-486721f062314f54ad765936a6258c2a |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T04:11:31Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-486721f062314f54ad765936a6258c2a2023-12-03T13:59:53ZengMDPI AGSymmetry2073-89942022-03-0114466010.3390/sym14040660Heisenberg Parabolic Subgroups of Exceptional Non-Compact <i>G</i><sub>2(2)</sub> and Invariant Differential OperatorsV.K. Dobrev0Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tsarigradsko Chaussee, 1784 Sofia, BulgariaIn the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebra <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mrow><mn>2</mn><mo>(</mo><mn>2</mn><mo>)</mo></mrow></msub></semantics></math></inline-formula>. We use both the minimal and the maximal Heisenberg parabolic subalgebras. We give the main multiplets of indecomposable elementary representations. This includes the explicit parametrization of the intertwining differential operators between the ERs. These are new results applicable in all cases when one would like to use <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mrow><mn>2</mn><mo>(</mo><mn>2</mn><mo>)</mo></mrow></msub></semantics></math></inline-formula> invariant differential operators.https://www.mdpi.com/2073-8994/14/4/660invariant differential operatorsHeisenberg parabolic subgroupsexceptional non-compact groups |
| spellingShingle | V.K. Dobrev Heisenberg Parabolic Subgroups of Exceptional Non-Compact <i>G</i><sub>2(2)</sub> and Invariant Differential Operators Symmetry invariant differential operators Heisenberg parabolic subgroups exceptional non-compact groups |
| title | Heisenberg Parabolic Subgroups of Exceptional Non-Compact <i>G</i><sub>2(2)</sub> and Invariant Differential Operators |
| title_full | Heisenberg Parabolic Subgroups of Exceptional Non-Compact <i>G</i><sub>2(2)</sub> and Invariant Differential Operators |
| title_fullStr | Heisenberg Parabolic Subgroups of Exceptional Non-Compact <i>G</i><sub>2(2)</sub> and Invariant Differential Operators |
| title_full_unstemmed | Heisenberg Parabolic Subgroups of Exceptional Non-Compact <i>G</i><sub>2(2)</sub> and Invariant Differential Operators |
| title_short | Heisenberg Parabolic Subgroups of Exceptional Non-Compact <i>G</i><sub>2(2)</sub> and Invariant Differential Operators |
| title_sort | heisenberg parabolic subgroups of exceptional non compact i g i sub 2 2 sub and invariant differential operators |
| topic | invariant differential operators Heisenberg parabolic subgroups exceptional non-compact groups |
| url | https://www.mdpi.com/2073-8994/14/4/660 |
| work_keys_str_mv | AT vkdobrev heisenbergparabolicsubgroupsofexceptionalnoncompactigisub22subandinvariantdifferentialoperators |