In studying residual automorphic representations, we need to parametrize the image of normalized local intertwining operators. This has been done by Moeglin in the case of the residual spectrum attached to the trivial character of the torus for split classical groups. In this paper, we extend her result to non-trivial characters of the torus. To do this, we use Roche’s Hecke algebra isomorphism...

We construct explicitly the q-vertex operators (intertwining operators) for the level one modules V (Λi) of the classical quantum affine algebras of twisted types using interacting bosons, where i = 0, 1 for A (2) 2n−1, i = 0 for D (3) 4 , i = 0, n for D (2) n+1, and i = n for A (2) 2n . A perfect crystal graph for D (3) 4 is constructed as a by-product.

New deformed affine algebras A~,η(ĝ) are defined for any simply-laced classical Lie algebra g, which are generalizations of the algebra A~,η(ŝl2) recently proposed by Khoroshkin, Lebedev and Pakuliak. The structure of the associated Hopf family of algebras is specified and bosonic representations for A~,η(ĝ) at all positive integer levels are obtained. For the special case of g = slr+1, (r + 1)...