例句與造句

1. Their homomorphisms correspond to invariant differential operators over flag manifolds.
2. The motivation for their study is that their homomorphisms correspond to invariant differential operators over generalized flag manifolds.
3. A classification of all linear conformally invariant differential operators on the sphere is known ( Eastwood and Rice, 1987 ).
4. Aside from the obstruction tensor, the ambient construction can be used to define a class of conformally invariant differential operators known as the GJMS operators.
5. Recently, these resolutions were studied in special cases, because of their connections to invariant differential operators in a special type of Cartan geometry, the parabolic geometries.
6. It's difficult to find invariant differential operator in a sentence. 用invariant differential operator造句挺難的
7. In an invariant differential operator D, the term " differential operator " indicates that the value Df of the map depends only on f ( x ) and the derivatives of f in x.
8. Conjugation is an action by automorphisms, i . e ., it commutes with the group structure, and this induces linear actions on naturally derived objects, such as its Lie algebra, and the algebra of left-invariant differential operators.
9. All linear invariant differential operators on homogeneous parabolic geometries, i . e . when " G " is semi-simple and " H " is a parabolic subgroup, are given dually by homomorphisms of generalized Verma modules.
10. To relate the above two cases : if \ mathfrak { g } is a vector space as abelian Lie algebra, the left-invariant differential operators are the constant coefficient operators, which are indeed a polynomial algebra in the partial derivatives of first order.
11. Indeed, the commutativity of the commutant implies that the simultaneous eigenspaces of the algebra of invariant differential operators all have dimension one; and the polynomial structure of this algebra forces the simultaneous eigenvalues to be precisely those already associated with Harish-Chandra's formula.
12. The center Z ( \ mathfrak { g } ) consists of the left-and right-invariant differential operators; this, in the case of not commutative, will often not be generated by first-order operators ( see for example Casimir operator of a semi-simple Lie algebra ).
13. A distribution on a group " G " or its Lie algebra is called an "'eigendistribution "'if it is an eigenvector of the center of the universal enveloping algebra of " G " ( identified with the left and right invariant differential operators of " G ".
14. If \ mathfrak { g } is the Lie algebra corresponding to the Lie group, then U ( \ mathfrak { g } ) can be identified with the algebra of left-invariant differential operators ( of all orders ) on; with \ mathfrak { g } lying inside it as the left-invariant vector fields as first-order differential operators.