Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772300 | Journal of Functional Analysis | 2017 | 45 Pages |
Abstract
During the last two decades, great efforts have been devoted to the calculation of the local theta correspondence for reductive dual pairs. However, uniform formulas remain elusive for real dual pairs of type I. The purpose of this paper is twofold: to formulate an explicit version of induction principle for dual pairs (O(p,q),Sp(2n,R)) with p+q even, and to apply it to obtain a complete and explicit description of the local theta correspondence when p+q=4. Our approach is very elementary by analysis on the infinitesimal characters and K-types under the theta correspondence.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Xiang Fan,