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&...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/4/660 |
| Summary: | 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. |
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| ISSN: | 2073-8994 |