REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

ABSTRACT: This talk is concerned with Eisenstein series on the n-fold cover of a classical group, which are defined over a field containing enough roots of unity.  The associated automorphic representations are the global analogues of principal series. As we shall explain, the contributions to their Whittaker coefficients at a good prime p are sums of certain Gauss sums mod p^{h_i} where the h_i are the lengths of root strings for certain Kashiwara lowering operators.  And there is a natural link to MV polytopes. Parts of this project are joint with Brubaker and Bump, with Zhang,and with Brubaker.