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Schubert Eisenstein Series
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 136, Number 6, December 2014
- pp. 1581-1608
- 10.1353/ajm.2014.0046
- Article
- Additional Information
We define Schubert Eisenstein series as sums like usual Eisenstein series but with the summation
restricted to elements of a particular Schubert cell, indexed by an element of the Weyl group. They
are generally not fully automorphic. We will develop some results and methods for ${\rm GL}_3$ that may be
suggestive about the general case. The six Schubert Eisenstein series are shown to have meromorphic
continuation and some functional equations. The Schubert Eisenstein series $E_{s_1s_2}$ and $E_{s_2s_1}$
corresponding to the Weyl group elements of order three are particularly interesting: at the point where
the full Eisenstein series is maximally polar, they unexpectedly become (with minor correction terms added)
fully automorphic and related to each other.