A commutativity criterion for certain algebras of invariant differential operators on nilpotent homogeneous spaces
| Autor: | Bernard Magneron, Salah Mehdi, Gérard Lion, H. Fujiwara |
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| Rok vydání: | 2003 |
| Předmět: |
Discrete mathematics
Pure mathematics General Mathematics Simple Lie group 010102 general mathematics Adjoint representation Zonal spherical function Universal enveloping algebra (g K)-module 01 natural sciences Graded Lie algebra Lie conformal algebra 010104 statistics & probability Unitary representation 0101 mathematics Mathematics |
| Zdroj: | Mathematische Annalen. 327:513-544 |
| ISSN: | 1432-1807 0025-5831 |
| Popis: | Let G be a connected, simply connected real nilpotent Lie group with Lie algebra g, H a connected closed subgroup of G with Lie algebra h and f a linear form on g satisfying f( (h, h)) ={ 0}· Let χf be the unitary character of H with differential √ −1f at the origin. Let τf be the unitary representation of G induced from the character χf of H. We consider the algebra D(g, h ,f) of differential operators invariant under the action of G on the bundle with basis G/H associated to these data. We show that D(g, h ,f) is commutative if and only if τf is of finite multiplicities. This proves a conjecture of Corwin-Greenleaf and Duflo. Mathematics Subject Classification (1991): 43A80, 43A85, 22E25, 22E27, 22E30 |
| Databáze: | OpenAIRE |
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