Solvability of left invariant differential operators on nilpotent lie groups

1984 ◽  
pp. 23-59 ◽  
Author(s):  
Lawrence Corwin
Keyword(s):  
Lie Groups ◽  
Differential Operators ◽  
Nilpotent Lie Groups ◽  
Invariant Differential Operators ◽  
Invariant Differential

scholarly journals INVARIANT DIFFERENTIAL OPERATORS FOR NON-COMPACT LIE GROUPS: PARABOLIC SUBALGEBRAS

2008 ◽  
Vol 20 (04) ◽  
pp. 407-449 ◽  
Author(s):  
V. K. DOBREV
Keyword(s):  
String Theory ◽  
Quantum Group ◽  
Lie Groups ◽  
Differential Operators ◽  
Explicit Construction ◽  
Compact Lie Groups ◽  
Invariant Differential Operators ◽  
Group Settings ◽  
Parabolic Subalgebras ◽  
Invariant Differential

In the present paper, we start the systematic explicit construction of invariant differential operators by giving explicit description of one of the main ingredients — the cuspidal parabolic subalgebras. We explicate also the maximal parabolic subalgebras, since these are also important even when they are not cuspidal. Our approach is easily generalized to the supersymmetric and quantum group settings and is necessary for applications to string theory and integrable models.

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