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Invariant Differential Operators and Weyl Group Invariants

Chapter
Part of the Progress in Mathematics book series (PM, volume 101)

Abstract

In this research announcement we describe the relationship between the algebra Z(G) of bi-invariant differential operators on a simple noncompact Lie group G and the algebra D(G/K )of invariant differential operators on the symmetric space G/K associated with G (cf. §4). The natural map µ: Z(G) → D(G/K) turns out to be surjective except in exactly four cases. These cases involve the exceptional groups and for them the relationship between Z(G) and D(G/K) is quite complicated. However for all cases of G/K, each DD(G/K) is the “ratio” of two µ(Z 1) and µ (Z 2) (with Z 1,Z 2Z(G)). See Theorem 4.1.

Keywords

Symmetric Space Spherical Function Quotient Field Noncompact Type Invariant Differential Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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